Top of page Quotations, photos, book and epub, aim of this essay
Publications
Unpublications
Not officially published short articles, notes, and the 2014 student essay bundle with which this all began

Background

16 October 2021
Young William Rowan Hamilton - hyperpolyglot
2 October 2021
William Edwin and the Chatham Market Guide
29 August 2021
The word ‘Quaternion’
07 August 2021
Hamilton’s godfather, Sydney Rowan Hamilton
14 July 2021
Hamilton’s Scottish or rather Irish descent, and Dr. James Hutton
26 September 2020
The error or flaw in Laplace’s Mécanique Céleste
23 August 2020
Lady Hamilton’s grave
3 May 2020
Graves’ opinion about Lady Hamilton, and apparent disagreements
25 April 2020
Lady Helen Hamilton’s crushed reputation
24 November 2019
Hamilton’s intellect, Grace McFerrand, and why Archibald Hamilton did not attend College
11 November 2019
A terrible hailstorm in 1850, and Biela’s comet
23 October 2019
Dunsink Observatory, the Meridian room, and again Hamilton’s birth house
19 October 2019
Lady Hamilton’s last years, a pension and Allendale Cottage in Drumcondra
16 October 2019
A game and locations in Hamilton’s life, quaternions and spacecraft
16 August 2019
Trinity Library; letters and photos
3/4 August 2019
The IHoM5 in Maynooth
15 June 2019
Reverend Benjamin Williams Mathias
19 May 2019
Uncle James, his family and the Diocesan School
4 May 2019
Illnesses and astronomy
18 January 2019
An article about the largely ignored influence of Helen Bayly and Catherine Disney on Hamilton’s life
11 November 2018
Photos of Hamilton and his notebook, also showing Graves’ blue pencil
20 September 2018
Calculating, quaternions, Gibbs and computers
30 June 2018
Extreme honesty and eccentricity, a happy marriage and drinking prowess, and still evolving gossip
15 June 2018
Hamilton and Coleridge
8 June 2018
Astronomy in 1848; Hamilton’s visit to Parsonstown
31 March 2018
De Vere about Hamilton’s affection for his wife
11 February 2018
The siblings of Hamilton’s father, and the Rowan name
4 February 2018
Patrick Wayman, our gossip article, and the “fabrication, or at any rate a gross exaggeration” of the uneaten meals in Hamilton’s study
2 February 2018
Macfarlane, William Edwin Hamilton, alcohol, gossip, history in need of corrections in case of new insights
29 January 2018
Ellen de Vere, Miss Ellis of Abbotstown, and parents bereaved of nearly all their children
12 January 2018
Hamilton’s “splendid meteor”
7 January 2018
Lady Wilde, and her son Oscar having been born on the birthday of the quaternions
21 December 2017
Hamilton’s formulation of geometrical optics as the marriage between the wave theory of Fresnel and the ray method of Newton
12 December 2017
Publication of ‘A most gossiped about genius: Sir William Rowan Hamilton’
22 November 2017
Publication of the corrected version of ‘A Victorian Marriage’
26 August 2017
The death of Edward Senior in 1865:
most likely the second fatal train accident in Dublin
7 July 2017
Summerhill House, Langfords and Longfords, and Hamilton’s account from within the house
31 October 2016
Paper copies, an epub version of ‘A Victorian Marriage’, and ereaders
18 September 2016
Files sent to the printer, and a search for Hamilton’s birth house
22 October 2015
Attending the Hamilton Walk in Dublin
15 October 2015
Having finished the essay ‘A Victorian Marriage’, corrections are still needed
2 September 2015
The 150th anniversary of the death day of
Sir William Rowan Hamilton (1805-1865)


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Creative Commons License  This work is licensed under a CC BY 4.0 International License



Entrance page. This website, Hamilton’s work, summary of A Victorian Marriage

Catherine Disney. Background information, James and Jane Barlow

Photos of people in Hamilton’s biography

Miscellaneous. Hamiltoniana, Climate and Nature, and a bit of Physics


My books can be read in the Internet Archive’s BookReader:

A Victorian Marriage : Sir William Rowan Hamilton

Catherine Disney : a biographical sketch


Contact







A Victorian Marriage : Sir William Rowan Hamilton







Hamilton essay, books



Sir William Rowan Hamilton (1805-1865) doubtlessly was Ireland’s most ingenious mathematician. Hamilton’s work has always been highly praised, and he was knighted in 1835 for his theoretical discovery of conical refraction. Yet his private life has been heavily gossiped about; he is often seen as having been an unhappily married alcoholic.
His own description of the discovery of the quaternions, 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. That resulted in the writing of this essay, in which it has been shown that he did have a good marriage, and that according to current standards he was by no means an alcoholic.





Hamilton was indeed a most admirable person, and a most truly amiable and high-souled one. Nothing but so much greatness could have made so much enthusiasm only what was natural — and nothing but so much enthusiasm could have carried him on to so much greatness.

— John Frederick William Herschel




[Helen Bayly] brought calm to [Hamilton’s] affections; she won the good opinion of his friends; and she became to him the centre round which the pleasures, the duties, and the hopes of home were gathered.

— Robert Perceval Graves




I know really scarcely anyone who seems more universally to have “won golden opinions” from her extensive circle of acquaintance [...]. Of her present guests and your aunt [your amiable wife] has won hearts — and hearts not easily won. I am preparing to yield mine, or rather have done so.

— Uncle James Hamilton




His whole happiness seems to be in making others happy; indeed any woman is blessed to be married to such an affectionate kind creature as Hamilton.

— Helena Maria Hamilton née Bayly




As to [Miss Bayly’s] beauty, I may unconsciously exaggerate that in my present state of feeling, and I must own that it did not strike me at first nor always, though lately it has much impressed me. But her mind I was pleased with from the first [...]. Spirituality, including but not confined to religion, appeared early and still appears to me to be its characteristic; and though she is not a person of brilliant or highly cultivated intellect, yet I have always found that I converse with her with pleasure, and that my own mind is excited and refined by her society.

— William Rowan Hamilton



The essay can be read online in The Internet Archive’s BookReader, see the link on top of this page. In case offline reading is preferred, it can be downloaded below as a pdf (left) or an epub (right). For further publications, see Publications.



A Victorian Marriage : Sir William Rowan Hamilton              A Victorian Marriage : Sir William Rowan Hamilton




“I have at last read the whole of your big book, and am most impressed with the amount of effort and research you have put into it. Congratulations! I do think you have made your case — Hamilton was not an alcoholic, and he loved his wife Helen.”

— Charles Mollan, historian of Irish Science, formerly Science Officer of the Royal Dublin Society.


“A former student recently sent me a copy of Hankins’ biography of Hamilton. He’d picked it up in a flea-market and decided to pass it on to me. When I got to the chapter about Hamilton’s love-life I just had to go back and reread what you had to say about it. It is really terrible that such a distortion of the facts could have become the accepted version.”

— Anthony O’Farrell, professor emeritus and initiator of the yearly Hamilton Walk.




The books have only been printed in hardback copies, which cost €62.50 each (not including postal charges). In case paper books are indeed preferred: they can be ordered by filling in a form at BoekenGilde: A Victorian Marriage : Sir William Rowan Hamilton. Clicking on the box: Beschikbaarheid opvragen = Request availability, shows the form in which Naam = Name, E-mailadres = E-mail address, Gewenst aantal boeken = Desired number of books, Versturen = Send. It will be read both by BoekenGilde and me; if we receive ten requests, the essay will be printed in an again small edition.
The book is available open access at Googe Books and the Internet Archive. I also made a “project” about Hamilton on ResearchGate where comments can be made if logged in.

The epub was made with a beautiful template my nephew made for me. But because Google Books and some e-readers require epub 2 or 3, I made two additional versions, A_Victorian_Marriage_-_Sir_WRH_2.0.1.epub, A_Victorian_Marriage_-_Sir_WRH_3.0.1.epub

For English and Dutch summaries, and further publications, see Publications

For some information about me see:  ORCID iD icon



The fourfold aim of this essay is to

— show that, contrary to general belief, Sir William Rowan Hamilton had a good marriage, that in fact large parts of his marriage were fairly happy. It is discussed where the idea of his marriage as having been an unhappy one came from, and it is shown that according to current standards he was by no means an alcoholic.

— emphasize that people should be looked at within the context of their time and circumstances. That Lady Hamilton leaving her children because she was ill was something which was very likely done on doctor’s orders; no-one then knew anything about the impact it could have on children’s later lives. Or that the Hamiltons lived at an observatory which was built at a remote, dark, and elevated place, in a time in which light bulbs, radio, television, telephone and computers had not been invented yet. Which means that in the years that the children still were young, when Hamilton was in England every evening Lady Hamilton would be alone in her candle lit room, the servants and the personnel being with the sleeping children, talking to each other, or being at their own homes. Such circumstances would make not only Lady Hamilton but almost anyone prefer to visit a neighbouring sister.

— argue that although on the one hand it is important to regard people in the context of their time, on the other hand that should be kept within reasonable limits; it is perfectly all right to recognize that Hamilton may have been judged unfairly in his days, that if he would have lived nowadays no-one would have given his behaviour any second thoughts. It is therefore justified to speak more positively about him than it was done in his days; Hamilton just seems not to have been willing to adjust to a rapidly changing society. As still happens nowadays: many people do not want to adapt to drastic changes in social behaviour, especially when the social rules or habits during childhood or early adulthood were considered just fine.

— draw attention to the fact that in Victorian times especially women were extremely harshly judged, and so was Lady Hamilton. During those years women were expected to be, by nature, warm, tender, caring, poetic and literary, but many women did not come up to these standards being logical, stubborn, practical, headstrong, technical, or just not poetic. Their condemnation is something which does not have to be repeated now; these are not Victorian times anymore.






Lectures on and Elements of Quaternions by Sir William Rowan Hamilton


These copies of the two books on Quaternions written by Sir William Rowan Hamilton (1805-1865) are kept at the Special Collections of Utrecht University Library. They can both be read online at the Internet Archive: Lectures on Quaternions (Dublin, 1853) and Elements of Quaternions (Dublin, 1866).

In July 2015 Frans Sellies, one of my colleagues at the Library, showed me the books and very kindly made the beautiful photographs shown above. To see the books in reality was more touching than I had expected, and in order to do something symbolic with having seen them all the colours of this website come from Hamilton’s books as shown on the Internet Archive, and those of the logo come from photographs Frans made of the books. For Frans’ photos see his flickr page.







Publications



2021 - Symposium Presentation - Sir William Rowan Hamilton : the influence of the 1880s temperance struggles on his posthumous reputation
Online presentation on the fourth day of the BSHM - CSHPM/SCHPM Conference, the 5-yearly joint conference of the British Society for the History of Mathematics and Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d'Histoire et de Philosophie des Mathématiques, in collaboration with HOM-SIGMAA, the History of Mathematics Special Interest Group of the MAA. Online, coordinated through the University of St Andrews, Scotland, 12-15 July 2021.


2019 - RTÉ Brainstorm Contribution - How a 19th century Irish mathematician helped NASA into space
With Colm Mulcahy and Michel Destrade. Written as a celebration of 176 years of quaternions and published by RTÉ’s Brainstorm on Hamilton Day.


2019 - Symposium Presentation - A biographer’s opinion as primary source : the strange case of Sir William Rowan Hamilton
Presentation given on the second day of the IHoM5, the joint Irish History of Mathematics (IHoM) and British Society for the History of Mathematics (BSHM) Conference, held at Maynooth University on 1 and 2 August 2019.


2019 - Book - Catherine Disney : a biographical sketch - viii, 135 pages : illustrations, portraits, maps ; 25 cm.
I wrote this sketch in order to do Catherine honour; she had a very difficult life because, while in love with Hamilton, she was forced to marry someone else. In later years learning how terribly unhappy she was caused Hamilton much distress. That, however, did not at all mean that he had only loved her, as has been claimed, the story about Catherine’s unhappiness simply is a terrible story. Forcing people into marriage should be impossible.
This book can also be read, as pdf or epub, here at Google books, or here at the Internet Archive.


2018 - Journal article - Helen Bayly and Catherine Disney as influences in the life of Sir William Rowan Hamilton
This article has been published in the Winter 2018 issue of Bulletin of the Irish Mathematical Society. For errata see Utrecht, 18 January 2019.


2018 - Magazine Article - Astronomy in 1848
This is an English translation of a short article, Sterrenkunde in 1848, which was published in the June issue of Zenit, the popular science magazine for astronomy, meteorology and space research, and organ of the KNVWS, the Royal Dutch Association for Meteorology and Astronomy. See also Utrecht, 8 June 2018. The article describes one of Hamilton’s visits to Parsonstown, where Lord Rosse had built the Leviathan telescope, then the largest telescope in the world.


2018 - Journal Article - On an 1850 report of a fireball from the Scorpiid-Sagittariid Complex
In 1850 Hamilton saw a ‘splendid meteor’, and he wrote a short report about it in a local newspaper. It appeared to be the first known report of a meteor of that complex. This article has been published in WGN, Journal of the International Meteor Organization. See for some more information Utrecht, 12 January 2018. A Dutch announcement of the article, een Nederlandse bekendmaking van het artikel, can be found here: Over een verslag uit 1850 van een zeer heldere meteoor.


2017 - Journal Article - A most gossiped about genius: Sir William Rowan Hamilton
With Steven Wepster. Published in the British Journal for the History of Mathematics, in this article first an English summary of the 2015, and in 2017 corrected, essay has been given. Using six books, published between 1902 and 2008, the second part of this article shows how Hamilton’s private life became the caricature it is nowadays. For this article see also Utrecht, 12 December 2017.


2017 - Book - A Victorian Marriage : Sir William Rowan Hamilton - xii, 508 pages : illustrations, portraits ; 25 cm.
This is the book, or essay, with which this project began. I published the first version in 2015, and soon saw it needed quite some corrections. What I aimed for is to show convincingly that Hamilton was happily married, was not an alcoholic, and had an understandable grief about the terrible fate of his first love Catherine Disney.
This book can also be read, as pdf or epub here at Google books. A Dutch summary, een Nederlandse samenvatting, can be found here: Een Victoriaans Huwelijk.





Unpublications

Not officially published short articles and notes



About Graves’ claim that when thirteen, Hamilton “was in different degrees acquainted with thirteen languages”16 October 2021

Sir William Rowan Hamilton’s godfather, Sydney Hamilton Rowan07 August 2021

Hamilton’s descent and Dr. James Hutton14 July 2021

William Hamilton and the ‘flaw’ in Laplace, the flawed story about it, and William’s proof26 September 2020

Lady Hamilton’s descent25 April 2020

Archibald Hamilton and education24 November 2019

Grace McFerrand24 November 2019Updated July 2021

Uncle James - theologian and linguist24 November 2019

Biela’s Comet11 November 2019

The twenty places in Hamilton’s Ireland as given in the game on Hamilton’s Ireland. Written for Ireland’s Maths week, 12-20 October 2019.

The family of Uncle James Hamilton of Trim19 May 2019

Sir William Rowan Hamilton : Illnesses and astronomy4 May 2019

The Hamiltons of Jervis Street and the name Rowan11 February 2018Revised July 2021

About the ownership of Summerhill House, where Hamilton met Catherine7 July 2017

Lower Dominick Street18 September 2016.


Van Quaternionen tot VectoranalyseSummer 2014
The bundle with which this Hamilton project began. Unfortunately, it is in both Dutch and English, which means that there will always be someone who cannot read it all.
Not knowing then what I know now, I now would have chosen a real photo of Hamilton. Also, the photo of Green is erroneous, no photo of him seems to exist. He died in 1841, only three years after the first photo was made on which people can be seen. (Btw, is in that photo a child peeping through the curtains, in the left upper window of the white house? Perhaps the child saw the photographer and wondered what that strange man was doing with that little box.)





Background information



Utrecht, 16 October 2021 — Young William Hamilton as a hyperpolyglot

Today is my seventh Quaternion day; I started this website in September 2015, on Hamilton’s 150th death day, and walked the Hamilton walk in October 2015. From then on I have researched many myths about Hamilton’s private life, and found more erroneous assumptions than I had expected.

In 2014 I wrote a chapter about Hamilton’s marriage for a students’s essay about the History of Vector Analysis because I could not believe that such a peaceful walk as that on 16 October 1843 could be made in such an unhappy marriage as it was claimed to be. But I then still accepted the idea that while writing the Lectures between 1848 and 1853, Hamilton had had a very difficult time in connection with Catherine Disney, and that he then, temporarily, leaned towards alcoholism. That changed when I was writing my AVM and started to recognise the many connections and nuances in Graves’ enormous biography. It changed even further when I was preparing my biographical sketch about Catherine and looked at what happened from her point of view. Hamilton had been distressed about her indeed, but who would not be, discovering that someone who once was so close is so terribly unhappy, betrayed by her own family and imprisoned by forced promises at the altar.

But there are many more myths to go. One of the myths is whether or not Hamilton was, “when thirteen years old” “in different degrees acquainted with thirteen languages,” as was claimed by Hamilton’s later biographer Graves, in a ‘portrait’ he wrote about Hamilton in 1842.* Although indirectly, it is also mentioned by Hamilton’s father Archibald by giving, in a letter to a friend, the languages his son was studying. Yet his claim has been doubted, as just having come from a father boasting about his “prodigy of a son.”

* The Dublin University Magazine had decided that Hamilton “must take his place in the series of memoirs of distinguished Irishmen,” and although Graves then lived in England for six or seven years already, Hamilton “requested me to undertake the friendly office, and gained my consent.”

I started a search in Graves’ biography, to find who exactly said what and when. It appeared that the claim by Hamilton’s father only seemed to be extravagant because Jane Sydney Hamilton, called aunt Sydney, had died in 1814, while she was the writer of most of the letters about young Hamilton’s progress. She died in Dublin, where she had been taken care of by Hamilton’s parents, in October 1814; her last given letter was from June 1814. But later biographers may not have been aware of her death at that time because Graves only mentioned it when introducing aunt Sydney in the first chapter of his biography.

Strangely enough, the list of languages in the 1880s biography appreared to be not exactly the same as that in the 1842 portrait, which led to the realisation that there was indeed a difference in how the biography and the portrait had come about. When Graves published the first volume of his biography in 1882, he had read all Hamilton’s personal correspondences including those with his family, and therefore also the letter from Archibald Hamilton to his friend. But that was not the case in 1842, when Graves published the portrait, about which he wrote that preparing it “led to my paying [Hamilton] a visit at the Observatory for the purpose of gathering facts.” The portrait therefore gives Hamilton’s own account of his youthful studies.*

* Hamilton had no final say in the text. He mocked the list of languages, but did not deny or correct it.

Now adding up the languages Graves mentioned in his ‘portrait’ and the languages in the biography, I unexpectedly found even sixteen languages. I wrote an unpublication about it, with as I hope enough references to be convincing about my conclusion, that in our times Hamilton would have been a hyperpolyglot.



Utrecht, 2 October 2021 — William Edwin and the Chatham Market Guide

For William Edwin see also 2 February 2018, below

Lately Miguel DeArce sent me some scans of letters from the Hamilton collections in Trinity College Dublin Library, and to my utter surprise I recognised the handwriting in one of the letters; it was the handwriting of the first of the drafts in which Lady Hamilton thanked for the continuation of Hamilton’s pension, shown below, and appeared to be that of William Edwin Hamilton. Before having seen this letter I had supposed that the first draft had been written by his sister Helen Eliza because the pension would be shared with her, and because writing out Lady Hamilton’s full name seemed to indicate someone very close by. I adapted the text to this new find.

Strangely enough, searching in my files it appeared that I already had an 1865 letter by William Edwin, which was sent to me by one of the TCD Librarians. Wondering why I nevertheless had not recognised his handwriting in the draft, I compared it with the 1865 and 1882 letters of which it is certain that William Edwin wrote them. As a weak excuse, the draft and the 1882 letter do seem to me to be more similar to each other than to the 1865 letter.*

* The drafts and both letters are kept at Trinity College Dublin Library; the drafts together as 7762-7772/1698, the 1865 letter as 7773-7776/642, the 1882 one as 4015/117.

The letter was written in 1882, in Chatham, Ontario, at the offices of the newspaper Planet,* where William Edwin was a journalist and editor. In 1914 Sheriff J.R. Gemmill, then president of the Chatham Historical Society, wrote, after mixing him up with his father, that William Edwin “came to Canada in middle life, settling in the Muskoka District. Later he came to Dresden and edited the local paper there for a time; then to Chatham, where he directed the Tribune** until its demise. Failing regular employment on either of the existing papers, he published a small advertising sheet, “The Market Guide”, which appeared on Saturdays, and which the Editor faithfully distributed to the patrons of our far famed market for the benefit of his advertisers.”

* Starting as The Chatham Planet in 1851, the name of the newspaper seems to have changed a few times. In William Edwin’s time its proprietor was Syd Stevenson.

** About the Tribune, officially called the Chatham Tribune, Gemmill wrote that it was “started by Dobbyn, B.A., in or about 1880, and existed only a few troublous years.” It existed from 1877 until, apparently, 1882. William R. Dobbyn was a “Universalist clergy-man from New England,” later owner of the W.R. Dobbyn & Sons printing and publishing company. In my AVM I wrote that he was born in 1850 and died in 1922, but I cannot find the exact source any more. Yet he may have been this Dobbyn, the birth and death locations of his wives matching what is known about him.

Gemmill clearly did not know about William Edwin’s time at the Planet, and in his strange autobiography Peeps at my life William Edwin is neither elaborate nor always chronological. Combining the scarce facts about his early years in Chatham: he mentions that he came to Chatham in October 1880. He then was editor of the Tribune for eighteen months, that is until April 1882, which would be in accord with Gemmill’s account. Then for again eighteen months editor of the Planet, which would be until October 1883, and in accord with having written the letter at the offices of the Planet in November 1882. But he may have taken the periods very roughly, because it appears that he was still working at the Planet in 1884.

William Edwin started the Market Guide in September 1885. But Gemmill having called it a “small advertising sheet,” I had not expected to find it in the Chatham list, let alone that some issues would be online. William Edwin published it from 1885 until, most likely, his death in 1902. That it really is William Edwin’s paper can be seen on the first pages of this 1896 issue; “The Market Guide, 1000 Circulation Weekly. Personal Saturday distribution by W.E. Hamilton, B.A., T.C., D. Editor and Proprietor.” Volumes would be mailed to subscribers in Canada and the US, yet he also had subscribers “from Vancouver to Nova Scotia, and even beyond the ocean.”

Alexander Macfarlane wrote that for a time William Edwin drank too much, yet without giving any indication of when that was. Drinking more and more may have been a slow process, taking years, but if he lost the Planet editorship in early 1884, the time of really drinking too much will have started in early 1884. He took the gold cure, and according to Macfarlane he “was able to master his alcoholic enemy.”

William Edwin also features as an old alcoholic called Burnham in the 1924 autobiography of Augustus Bridle, but it is not known how accurate that is. It was suggested that the descriptions were from the late 1880s, and I had accepted that because the Chatham Market Guide had been described as next to nothing. But now having seen the three issues, it is hard to believe that writing and making such a paper, including collecting the advertisements, every week all by himself, can be done next to a day job and just sitting in bars being drunk, as the autobiography suggests. If William Edwin therefore took the gold cure before he started the Market Guide, his most alcoholic time will have lasted from early 1884 until early 1885.

It seems safe to suggests that Bridle combined William Edwin’s most alcoholic time with his later years, when he was selling the Chatham Market Guide. Temperance became very strict in Canada in 1878, and although apparently the gold cure was succesful, it has not been claimed that William Edwin became a teetotaller. The strict laws were only repealed in the 1920s; if Bridle was himself very temperate he may have been unsatisfied with the level of drinking William Edwin maintained.

That also holds for Macfarlane. Writing that William Edwin had ‘wasted years’ by his drinking, he suggested that totally being overcome by alcohol lasted much longer. Macfarlane having written his 1902 obituary of William Edwin in those very temperate times, a pattern can be recognised which also ruined the reputation of Hamilton Sr.: biographers writing about drinking in times of Temperance without giving details about how long it lasted. But the difference is that in Hamilton Sr.’s life not any sign of drinking can be found. No missing years, or months, or periods without hard work, not even missed meetings; the only information comes from his biographer Graves. That is different for William Edwin. He lost his job with the Planet in some undefined way; the time between early 1884 until the summer of 1885 does seem to be missing;* and there were first-hand witnesses, Macfarlane and Bridle, who wrote about it.

* In 1884 his Muskoka Sketch was published, by the Dresden Times Printing Company. But William Edwin will have written the Sketch earlier, perhaps even as early as the late 1870s when he still lived in Dresden, writing about his time in Muskoka.
The Muskoka Sketch was called “a pleasant and entertaining sketch.” About his Guide book & atlas of Muskoka and Parry Sound Districts it was said that he “described the Muskoka waterfalls in the most sublime terminology.” Apparently, I am not the only one who enjoyed his writings.

William Edwin’s alcoholic image clung to him, in an even more extreme way than in his father’s case. Although he had, before he became alcoholic, quite an influence as a journalist, his alcoholic image seems to have had as a consequence that not many people took the claims he made in his Peeps seriously. Much is unclear about William Edwin’s later years; what I could find is in my AVM, pp 360-376. Although he was defended by some people, others wrote quite condescending about him. It therefore was a surprise to see that he published the Chatham Market Guide apparently without interruption for in any case sixteen years.

Also surprising is that from his paper his later ‘respectabe life’ can be inferred, and he clearly enjoyed it. Only some months before his death he wrote, “After the council meeting, at the hospitable invitation of the Mayor, the Aldermen present and reporters of the Planet, Banner and Market Guide together with Mr. Cockburn of Toronto, enjoyed a feast of bivalves and other delicacies together with various games ad interchange of anecdotes. Mayor Sulman and his amiable consort, show the model host and hostess with that rare indefinable power of making their guests thoroughly at home. Viewing the spacious semi-circular entrance porch, the handsome rooms en route with their mantle pieces of rare and harmoniously blended marbles, and above all, the extensive library of well selected and handsomely bound books, we were tempted to break the 10th Commandment [Thou shalt not covet any thing that is thy neighbour’s], more especially when we entered a cosy little sitting room which could have made an ideal editorial sanctum whence to throw darts at the enemy. Before leaving, our host showed us one of his stamp albums which $1000 wouldn’t buy. Ald. Marshall does it next time.”

What I still would like to know is whether or not William Edwin wrote the text of the unofficial national anthem of Canada Maple Leaf, as he seems to claim on p. 8 of his Peeps. “In 1869, appeared my national song, written in Marbleton, and called the “Maple Leaf,” published first in the Belfast Newsletter, then in the Sherbrooke Gazette and Montreal papers, and which was set to music and sung at concerts in the eastern townships. A phrase in another of my Dominion songs, “For this is our Natal Day,” has been quoted by [Nicholas Flood] Davin and other patriotic orators. I got a very cordial letter from Sir George Cartier, approving of the “Maple Leaf.” Coincidentally, William Edwin was buried at Maple Leaf Cemetery in Chatham.



Utrecht, 29 August 2021 — The word ‘Quaternion.’

In 1841, having searched in vain for triplets to describe motion in three-dimensional space, in the first letter of the correspondence with Augustus De Morgan which would continue until Hamilton’s death, Hamilton wrote, “If my view of algebra be just, it must be possible, some way or other, to introduce not only triplets but polyplets.” He later mentionedsingles, couples, triplets,” to which quadruplets would seem to be a natural addition. Still, Hamilton called the objects he found on 16 October 1843 ‘Quaternions,’ and he even decided very quickly what to call them; it took him less than an hour.

Hamilton had started a new search in the second half or the last week of September 1843, and every morning in early October, on his coming down to breakfast, his sons asked him, “Well, Papa, can you multiply triplets?” Whereto he “was always obliged to reply, with a sad shake of the head: “No, I can only add and subtract them.”” On Monday 16 October he was walking along the Royal Canal on his way to a meeting of the Royal Irish Academy when Lady Hamilton joined him. She had perhaps driven to meet her husband at the Canal,* and she talked with him now and then. Yet an ‘under-current of thought was going on in his mind,’ and he suddenly realized what the solution should be. Apparently still walking he pencilled, just as he reached Broom Bridge, the basic formulae in the notebook she had given him in 1840, and happily or in any case ‘unphilosophically’ scratched the general formula on the bridge.

At the next bridge, Cross Guns Bridge (Westmoreland Bridge),** he apparently took a car and drove from the “neighbourhood of the turnpike to the Academy,” while Lady Hamilton may have returned home to tell the children that Papa had found his answer. They certainly will have sympathised; next to having asked him every morning, they would from then on call the bridge the ‘Quaternion Bridge.’*** During the ride in the car Hamilton examined whether the law of the moduli held for the new system (which he “wished for as a child might wish for the moon”). In the 1865 letter to his son Archibald he wrote, “Less than an hour elapsed before I had asked and obtained leave of the Council of the Royal Irish Academy, of which Society I was, at that time, the President - to read at the next General Meeting a Paper on Quaternions; which I accordingly did, on November 13, 1843.” And indeed, the word ‘Quaternions’ is in the Minutes of 16 October 1843.

* She may have let someone take her to the Canal; if she had had her horse with her Hamilton would have known.

** I heard about the second bridge, Cross Guns Bridge, at the Hamilton Walk in 2015, when Anthony O’Farrell told us about the turnpike and the ‘hackney stand’ at the bridge.

*** Calling Broom Bridge ‘Brougham Bridge’, as Hamilton did, may have been a family joke.

But it is not known why he chose to call them quaternions. Because of Hamilton’s poetic mind John Milton’s 1667 epic poem Paradise Lost is often mentioned as a possible source; Milton uses the word quaternion in line 181 of book 5. Also the Bible is suggested; Hamilton was deeply religious, and he already loved reading the Bible when still very young. The word quaternion is used in The Acts, 12:4.

Wondering how common the word was around 1843, the year of discovery, I did an Ngram search, which starts with 1500. Such a search is of course never complete; this one searches the titles in Google Books. Before Milton in 1667, the word quaternion was most often used around 1640; three times by Ben Jonson and two times Thomas Fuller in 1640 or rather, in publications from 1640. Clicking on the 1718-1828 box yielded 188 results, of which some are counted multiple times, and some are later publications. The list contains a surprise; the first books in the list are from the mathematician Charles Hutton who was supposed to be a relation of Hamilton’s mother Sarah Hutton, which he was not. In his 1785 Mathematical tables he used the word quaternion very straightforward, signifying the boxes in the logarithm table on p. 63, ‘spaces of four lines or numbers.’

Also in the list is Sir John Leslie, who wrote in 1817, in The Philosophy of Arithmetic, “But four, or the tetrad, was the number which Pythagoras affected to venerate the most. It is a square, and contains within itself all the musical proportions, and exhibits by summation all the digits as far as ten, the root of the universal scale of numeration; it marks the seasons, the elements, and the successive ages of man; and it likewise represents the cardinal virtues, and the opposite vices. The ancient division of mathematical science into Arithmetic, Geometry, Astronomy, and Music, was four-fold, and the course was therefore termed a tetractys, or quaternion.”

Apparently, the word quaternion was such a common word that the question how Hamilton knew about the word does not have to be answered further, leaving the question why he chose the word. The only time Hamilton did give something of an explanation was a rather general remark in a footnote; on p 111 of the Elements of Quaternions, written between 1858 and 1865, he writes, “As to the mere word, Quaternion, it signifies primarily (as is well known), like its Latin original, “Quaternio,” or the Greek noun τετρακτυς, a Set of Four: but it is obviously used here, and elsewhere in the present work, in a technical sense.” Not really an answer to the question posed here.

Pythagoras was a Greek philosopher who lived around -500, and his connection with the tetractys or quaternion, as mentioned by Leslie, was well-known; clicking on the 1500-1639 NGram box yields almost 700 hits, including the 1549 English translation of Desiderius ErasmusThe praise of Folie who also mentions, on p. 10, “Pythagoras quaternion,” in the original 1509 Latin “Pythagoricus quaternio.” In the 1641-1717 box is a book by André Dacier, The life of Pythagoras, with his Symbols and Golden verses, published in 1707, in which Dacier explains the origin of the Greek word tetractys. The book starts with a Life of Pythagoras. Having given Pythagoras’ Golden verses, in a footnote Dacier writes, “We have shewn in the Life of Pythagoras, that this Philosopher having learnt in Egypt the Name of the true God, the mysterious and ineffable Name, Jehovah, and finding that in the original Tongue it was compos’d of four Letters, translated it into his Mother Tongue by the Word Tetractys, the Quaternion, and gave the true Explication of it, saying that it properly signify’d, the Source of Nature that perpetually rolls along; for so the original Word signifies.

Also Hamilton knew about Pythagoras. In his younger years he was educated in the classics and was interested in mathematics and astronomy; already in 1820, when he was fifteen, he read Joanne Keill’s 1718 Introductio ad Veram Astronomiam. In the Preface Keill writes, in his own English translation, “Diogenes Laërtius [around +300] owns, that Thales [around -600], Pythagoras [around -500], Eudoxus [around -400], and many others went to [Egypt] to be instructed in the sidereal science. These men were not only the first but the greatest philosophers whom Greece produced; and from the same writer we know, that they who staid longest in that country, were most famous for their skill in Geometry and Astronomy after they returned home. So Pythagoras, who lived in society with the Egyptian priests seven years, and was initiated into their religion, carried home from thence besides several geometrical inventions, the true extent of the universe; and was the first who taught in Greece, that the earth and planets turned round the sun, which was immoveable in the center; and that the diurnal motion of the sun and fixed stars was not real, but apparent, arising from the motion of the earth round its axis. [...] Nicolas Copernicus was not only a diligent observer, but also a restorer of the ancient Pythagorean system.” The general view being that Copernicus in his 1543 De Revolutionibus Orbium Coelestium was the first to propose an heliocentric solar system, Hamilton will doubtlessly have been interested in such a claim.

What is certain is that Hamilton associated the word quaternion with Pythagoras. In 1846 he wrote a poem which Graves introduced, writing “This [...] sonnet [Hamilton] valued himself, and it will be valued by the reader, as one having a distinct individual character, uniting as it does Herschel and Hamilton in converse on Quaternions, and connecting this recent offspring of his mathematical thought by some imaginary lineage with the tetractys of Pythagoras.” The sonnet was preceded by lines from another sonnet which Hamilton later did not like too much, but Graves remarks that these lines were needed as a ‘grammatical introduction’ to the second poem. The sonnets together were called Recollections of Collingwood; John Herschel lived with his family at Collingwood, Kent,

Where all things graceful in succession come;
Bright blossoms growing on a lofty stalk,
Music and fairy-lore in Herschel’s home.

II.

The Tetractys.

Or high Mathesis,* with its “charm severe
Of line and number,” was our theme; and we
Sought to behold its unborn progeny,
And thrones reserved in Truth’s celestial sphere;
While views before attained became more clear:
And how the One of Time, of Space the Three,
Might in the Chain of Symbol girdled be:
And when my eager and reverted ear
Caught some faint echoes of an ancient strain,
Some shadowy outline of old thoughts sublime,
Gently He smiled to mark revive again,
In later age, and occidental clime,
A dimly traced Pythagorean lore;
A westward floating, mystic dream of Four.

* Hamilton may have alluded to mathematics in general, or to the idea by Leibniz and Descartes, of a universal science, or to the Mathesis universalis of John Wallis, published in 1657 in the first volume of the Operum Mathematicorum.

Yet here another concept is added, Truth. For Hamilton, Truth was one of the most important values in his life, which he connected with Science, and later with his wife. He called Poetry ‘Beauty’ and Science ‘Truth’, and in a poem he called Catherine Disney ‘Sweet Piety’, Ellen de Vere ‘Enthusiasm’, and Helen Bayly ‘Truth’. He felt that his epitaph should be “a labour-loving and truth-loving man,” he ultimately chose Science, and married Helen Bayly.

Searching online for these three concepts, Pythagoreanism, Quaternions and Truth, I found this ten-volume set, Ante-Nicene Fathers. It was published after Hamilton’s death, but it “brings together the work of early Christian thinkers.” On p. 241 of the fifth volume it is stated that “The Quaternion Exhibits “Truth”,” within the Hamilton narrative a remarkable connection. But it was said by Marcus, a contemporary of Irenaeus; they lived around +200. Marcus was a Gnostic, for the Christian thinkers a heretic, and on p. 235 Irenaeus calls him a “mere impostor.”

Hamilton and his Dublin colleagues knew about Marcus; George Salmon wrote the entry about Marcus in A dictionary of Christian biography and literature to the end of the sixth century A.D.. The question is therefore whether Hamilton would reject Marcus or gnosticism so fundamentally that he would not want to make a connection between his discovery and such a sense of Truth. But that certainly does not have to be the case; he wrote openly, “I do not feel in the least afraid, for myself, of reading anything. I have read atheistical books, infidel books, Socinian books, Protestant evangelical books, books by the Archbishop of Dublin, Protestant High-church books, Romanist books.”*

* This list is obviously partly in jest, and the context shows that De Vere’s conversion to Catholicism in 1851 did not cost him Hamilton’s friendship.

Concluding, Milton and his impressive poem does not seem to be necessary at all, because in Hamilton’s time the word quaternion was a quite regular word, connected to Pythagoras and the tetractys. What is left is the connotation with Truth. Hamilton decided for the word quaternion less than an hour after the discovery; obviously not having known beforehand what he would find it was a quick decision. The fact that Lady Hamilton had been with him at the moment of discovery, and that Hamilton explicitly mentioned that he wrote down the equations for the first time in a notebook which was given to him by her, allows for the idea that he associated them with her, and that his choice for Quaternions was connected with Truth. A totally unproven statement, but perfectly fitting the always romantic Hamilton.

Yet even though not proof, there are two enigmas which would hint at such a suggestion. Hamilton did not explain his choice for the word quaternion, and he kept silent about the last part of the walk, even though the distance between Broom Bridge and Cross Guns Bridge is two kilometres; twenty minutes are missing. He wrote that he “did actually pencil at the time, and just as I reached the Bridge here mentioned, the notes [in the pocket-book]. Then in a jolted handwriting, the same pencilled page contains these other notes, which were inserted while I was driving on that (to me memorable) Monday from the neighbourhood of the turnpike to the Academy.” There is nothing about the walk between the bridges, and Hamilton did not already start to check the law of the moduli even though he could have; he often enough read while walking. That might mean that he was not alone, which leaves room for a further possibility; that Lady Hamilton walked with him to Cross Guns Bridge, that they ecstatically talked about the discovery, and that she knew that he would call them after her before she returned to the Observatory.* It would certainly have been a loving reward for all the effort she had made, and as he “foresaw, immediately,” would have to make for many years to come, to allow for her husband’s intense studies, and tolerate his disappearing from her sight so often when he was in one of his mathematical trances.

The “Quaternions exhibiting Truth” would indeed be an answer to the enigmas why Hamilton never explained his choice for the word Quaternion,** and why he did not say anything about the last part of the walk. Telling people that it was a Gnostic association would perhaps not be appreciated too much, and having chosen it to honour his wife was doubtlessly not something he would like to explain. Giving some other beautiful reason was out of the question; it is known that Hamilton could not lie, but he could keep silent if he had to.

* When I asked Daniel Doyle about the sand sculpture, he explained that because Lady Hamilton was present at the moment of discovery he had assumed that she was her husband’s muse. He may have been more right than I had imagined before this search.


Note added September 2021: I completely overlooked a ‘popular account of the principles on which the Quaternion Calculus was founded,’ given in the appendix of the third volume of Graves’ biography in the form of an ‘Elementary Sketch.’ It was written after the publication of the Lectures on Quaternions in 1853, and in this sketch Hamilton writes about the naming of the Quaternions. “The word ”Quaternion” requires no explanation, since, although not now very commonly used, it occurs in the Scriptures and in Milton. Peter was delivered to “four quaternions of soldiers” to keep him; Adam, in his morning hymn, invokes air and the elements, “which in quaternion run.” The word (like, the Latin “quaternio,” from which it is derived) means simply a set of four, whether those “four” be persons or things.”

This explanation is similar to the above-mentioned remark in the Elements of Quaternions, and as dry as an explanation can be. Even though Hamilton mentions the Bible and Milton, he does not in any way connect his choice to them. As was also suggested above it is easy to imagine that that was intentional, to avoid having to tell a lie; it is hardly credible that such a deeply romantic man as Hamilton would, on such an extraordinary day, for the discovery about which he “foresaw, immediately” that it would profoundly influence and change his life, choose a name just for its literal meaning.



Utrecht, 07 August 2021 — Hamilton’s godfather, Sydney Hamilton Rowan

Some years ago, I do not remember when exactly, I found Archibald Hamilton Rowan’s death record. And I was surprised; he died in November 1834. I knew that Graves had written a quite indignant piece about a letter, as he supposed written by Rowan, in which Hamilton had been congratulated with his knighthood. Clearly, that was impossible; Hamilton was knighted in 1835, and Rowan died in 1834. An enigma which I thought would be beyond my reach, and in my blog post of 11 February 2018 I described the problem and suggested that someone should read the letter.

When we were in Dublin in 2019, we made photos of that letter, but it appeared quite difficult to read, and for a long time I did not look at it any more. Lately having found a Hamilton genealogy while at the same time slowly becoming more used to reading such handwritings, I decided to make a new effort. Having deciphered the letter, it all fell in place very smoothly.

There did not appear to be any reason to assume it must have been written by Archibald Hamilton Rowan himself; it can be surmised that seeing the name Hamilton Rowan, Graves reacted as if stung by a wasp, therefore not thinking about checking the dates. Searching the Hamilton genealogy which was published in 1867, around the same time that Graves started to write the biography, the only Hamilton Rowans were the members of Archibald Hamilton Rowan’s family. Rowan’s eldest son Gawin died in the same year as his parents, 1834, before Hamilton was knighted. The writer of the letter mentioned his sons, which means that he cannot have been Rowan’s third or fourth son; they died without issue. Having been born in 1801 the youngest son was only four at the time of the baptism, which means that the only Hamilton Rowan who could have stood as a sponsor at the baptism was Sydney Hamilton Rowan. Finally, reading in the letter that he was “father of ten children” which appeared to be in complete accord with the genealogy, did not leave much further doubt.

I wrote a short non-publication about it, and while writing and reasoning, taking into account how children were named then, I again arrived at the conclusion that Sir William Rowan Hamilton was most likely named after his early deceased uncle, Arthur Rowan Hamilton.



Utrecht, 14 July 2021 — Hamilton’s Scottish or rather Irish descent, and Dr. James Hutton

When searching for the family of Hamilton’s mother Sarah Hutton I found something unexpected; that Peter Guthrie Tait (here on the left), when he claimed that Sarah had been a relative of Dr. Hutton, will not have had the English mathematician Charles Hutton (1737-1823) in mind as Graves assumed (although he had his doubts), but the Scottish geologist James Hutton (1726-1797). Mentioning a relationship between Hamilton’s mother and ‘Dr. Hutton’ while claiming Hamilton for Scotland, having been related to the English Charles Hutton would not contribute to that claim, but one with the Scottish James Hutton would. It is shown in my unpublished Hamilton’s descent and Dr. James Hutton that the assumption that Tait was writing about Charles Hutton seems to have come from a train of earlier assumptions, as most of the errors in Hamilton’s story did, and still do, as shown in our gossip article.

Next to the assumption that Tait thus may have been right about ‘Dr. Hutton’ (the Scottish records should be searched), the conclusion about Hamilton’s descent is that both the Hamiltons and the Huttons came to Ireand in the 1600s. His paternal grandmother Grace MacFerrand was Scottish, and his maternal grandmother, Mary Ann Guinin, appears to have been French. It was marvellous to find her marriage record and therewith her last name, which was supposed to have been Guinant or Guissand. But I did not look at her descent yet.



Utrecht, 26 September 2020 — The error or flaw in Laplace’s Mécanique Céleste

A well-known story about Hamilton’s early mathematics is that in 1822, when he was sixteen years old, he discovered an error in the Mécanique Céleste by Pierre-Simon Laplace, and that showing his find to John Brinkley, who in 1788 he had graduated from Cambridge as Senior Wrangler and now was Royal Astronomer at Dunsink, the latter was impressed.

In my AVM I had not given much attention to such stories, on the one hand because I did not write about Hamilton’s mathematics, and on the other hand because it was generally agreed that Hamilton had a happy childhood; to discuss the contemporary view on his married life I therefore had not much need for it. But lately searching for his youthful astronomy, I found that the story about Laplace’s “error” was not so straightforward as it seems. The problem here is that when Hamilton’s biographer, Robert Graves, became emotional, indignant or in awe, he neglected the general chronology of the biography, causing much confusion.

In the first volume of his biography, while describing 1819, Graves writes that Hamilton, thirteen years old and celebrating holidays at his father’s house in Booterstown, wanted to remain there a bit longer. “One of these grounds was, that he might have the opportunity of repeating a visit to the Observatory which he had made on the day before [8 July 1819]. This was his first sight of the house which was to be his future home. He had walked out there with two apprentices of his father, carrying a lease as a letter of introduction to Dr. Brinkley, the Astronomer Royal; but to his disappointment the great man was absent, and he had to be contented with being shown the instruments by the assistant, and receiving some information respecting the comet which was then visible [the Great Comet of 1819]. The prayer of the petition [to be allowed to extend his stay at his father’s house] was granted, but it does not appear that the Observatory was again visited by him during his stay at Booterstown. When he did revisit it, years subsequently, he carried in his hand a more appropriate introduction, in the form of an original mathematical paper and a letter from his friend Mr. Kiernan.”

In April 1822, being sixteen years of age, Hamilton suffered from whooping-cough, and in May he was staying in Dublin with a cousin of his father and uncle James, called by Hamilton “Cousin Arthur”, who lived at Cumberland-street. Describing May 1822 Graves writes, “The change to Dublin [from Trim] proved beneficial to his health; and during the month of May which he spent there, we find him studying the Differential Calculus in the Treatise of Gamier, and making acquaintance with the Mécanique Céleste of Laplace. He signalised the beginning of this acquaintance with a great masterpiece by detecting a flaw in the reasoning by which Laplace demonstrates the parallelogram of forces. He wrote out his criticism at the instance of a friend, Mr. G. Kiernan, by whom it was shown to Dr. Brinkley; and thus was the seed sown of personal acquaintance with an elder of Science which had a most happy influence upon the future career of Hamilton. It will interest the mathematical reader to see a criticism which led to these results, and I am enabled by the kindness of Professor Hennessy to commit it to print from the original document, which was found by him inserted at the pages it refers to in the copy of the Mécanique Céleste which belonged to Dr. Brinkley, and which subsequently came into the possession of Mr. Hennessy. It is given in the Appendix.”

In these two paragraphs, when not reading very carefully, Graves seems to suggest that the “appropriate introduction, in the form of an original mathematical paper” was the “criticism” of Laplace, and that this paper was the direct cause of Hamilton’s personal acquaintance with Brinkley. But that is not exactly what he was saying, and it is not what happened.

As can be seen in the Appendix, Hamilton had found the ‘flaw in Laplace’s reasoning’ on 31 May 1822, and apparently Kiernan asked Hamilton to write it out so that he could show it to Brinkley, which he indeed did. On 31 October 1822, Hamilton wrote from Trim to Cousin Arthur, “When was Mr. Kiernan’s letter left at Cumberland-street? He tells me that “I forgot your ‘queries about Laplace’ for a long time,”” queries to which Graves comments that he was “not able to supply any information,” but about which Hamilton mentioned that he had also shown them to Boyton, his college tutor. Hamilton then wrote that Kiernan had continued, ““but at last I laid them before Dr. Brinkley, who said he thought them ingenious, and he was so good as to say that he would write an explanation for you. He also desired me to bring you to him, and that he would be happy to know you, and to show you the Observatory. This of course, you know, is a great honour.” And in a postcript: “I will have Dr. Brinkley’s answer for you when you call.” As my calling for it is out of the question [Hamilton then was in Trim], and I am rather anxious to see what Dr. Brinkley says — Do you know Mr. Kiernan? or would you like to call some day you are passing through Henry-street, and get it in my name? or should I write a note to him on Monday? In short I wish you would tell me what you think I had better do, as Mr. Kiernan’s politeness requires a return of civility.”* Apparently, Hamilton was still writing about the queries, not about the flaw in Laplace.

* From what Hamilton and Graves wrote about Kiernan it appears that he lived at Henry Street, and knew the astronomers Brinkley and John Herschel well. In January 1808 a George Kiernan, sixteen years old, born in Dublin as a son of George Kiernan, Pharmacopola, entered Trinity College Dublin. In 1819 a George Kiernan, living in Henry Street, became State Apothecary; also living in Henry Street this Kiernan will have been his father. And in Wilson’s almanac it can be seen that in 1783 there was a John Kiernan, living at 8 S. Anne Street, who also was an Apothecary, he may have been his grandfather. In 1783 also Hamilton’s grandfather, William Hamilton, was an Apothecary, at 30 Jervis Street, and it is reasonable to suggest that these people knew each other. If these connections are right, also Hamilton’s father and George Kiernan’s father may have known each other, as well as Cousin Arthur, after all, the letter was left at Cumberland Street. How Kiernan knew Brinkley was in any case through the RIA; in 1818 Kiernan was a member of the Royal Irish Academy, and Brinkley was its president from 1822 until 1835.

Then, still describing 1822, almost parenthetically Graves writes, “I find among the early mathematical manuscripts of Hamilton one entitled ‘Example of an Osculating Circle determined without any consideration repugnant to the utmost rigour of Analysis,’ and dated November 14, 1822; a second, without date, entitled ‘Osculating Parabola to Curves of Double Curvature’; and a third, dated December, 1822, of which the title is, ‘On Contacts between Algebraic Curves and Surfaces.’ These papers mark the year 1822, when he attained the seventeenth year of his age, as that in which Hamilton entered upon the path of original mathematical discovery. With the second and third of them in his hand, availing himself of the kind permission of Dr. Brinkley, he paid his first visit to him at the Observatory. Dr. Brinkley was impressed by their value, and desired to see some of the investigations in a more developed form; with this request Hamilton complied, by forwarding to him in the following month a paper entitled ‘Developments’; it was returned by him to Hamilton, and was in possession of the latter in the year 1841, but I have not discovered it among the manuscripts entrusted to me, nor I believe is it to be found in the Hamilton collection deposited in the manuscript-room of the Library of Trinity College.” And on 23 February 1823 Hamilton wrote to Cousin Arthur, “Perhaps you heard that Dr. Brinkley expressed his full approbation of my “Developments.””

Although Brinkley indeed received Hamilton’s “criticism” of Laplace, having put it into his copy of the Mécanique Céleste, it must be concluded that nothing is written here about Brinkley’s opinion about it; Brinkley reacted to the “queries” and was impressed by (the value of) the articles.


The ‘flaw’ and Hamilton’s very short proof

In William Hamilton and the ‘flaw’ in Laplace, the flawed story about it, and William’s proof I described the story above, and discussed the much shorter proof Hamilton gave about the parallelogram of forces, where the forces x and y are equal to the sides of the parallelogram, and the resultant force z is equal to its diagonal.


Parallelogram of forces

This ability to generalize, while even staying strictly within the boundaries of physics when needed, is what would define Hamilton as a mathematician; he knew the general quaternion formula on his walk along the Royal Canal before reaching the bridge, and De Morgan alluded to it when he wrote that whenever he sent Hamilton some work, the latter ‘generalized it at a glance.’ It is also why his work is still blossoming today; it is so generalistic that his mechanics easily lived on from Newton through Einstein and Schrödinger up to modern physics, and this quaternions are handled more easily by computers than linear algebra and vector analysis.



Utrecht, 23 August 2020 — Lady Hamilton’s grave

Updated 15 October 2020

Finally I found Lady Hamilton’s final resting place; she is buried at Mount Jerome, together with her husband. Strangely enough, although I am not religious, for me that is a relief because for such a pious couple, believing that through marriage they became one, I had been somewhat worried that she was buried somewhere else.

Every now and then searching for her grave, I had noticed that I could not find anything using her own name, I had to use her husband’s name, and then I in any case I found the advertisements announcing her death. So trying such a search again I found a remarkable advertisement in the Dublin Evening Mail of Tuesday 06 July 1869: “We are requested to state that Mr. W. E. Hamilton, eldest son of the late Sir William Hamilton, was prevented, by absence in the province of Quebec, Canada, from attending the funeral of the late Lady Hamilton, last month, at Mount Jerome Cemetery.”

Thereupon I contacted Mount Jerome Cemetery, and almost immediately received the confirmation that “The late Lady Hamilton was buried 05/06/1869” in the grave “which also holds her husband.” But something was unclear about the number, and to be certain in September Miguel DeArce contacted Mount Jerome again, to ask for Lady Hamilton’s burial record. Next to confirming that the Hamiltons are buried in the grave with number C116-3489 it appeared to hold a surprise; her cause of death was given, which until now I still did not know, “Disease of the heart.”

Another surprise was in the registry page for the grave, which was also sent by the contact person of Mount Jerome. The page shows that Archianna, Hamilton’s sister, was not buried in this grave.* That makes the question why Lady Hamilton is not inscribed on the tombstone even stranger. The transcription of the gravestone reads: ‘Here lie the mortal remains of Sir William Rowan Hamilton LL.D, Royal Astronomer of Ireland. He was born Aug. 4, 1805. He died Sept. 2, 1865. In the love of God waiting for the mercy of our Lord Jesus Christ unto eternal life, Jude 21. Also of his sister Archianna P.H. Hamilton. Also of his daughter Helen E.A. Hamilton, wife of the venerable John O'Regan, born August 11, 1840, died June 21, 1870. And of her husband the venerable John O'Regan, Archdeacon of Kildare, born Christmas Day, 1817, died Good Friday April 8, 1898. [...] Animae, Love is the fulfilling of the Law.** Erected by his surviving family.’

Searching for what may have happened, causing Hamilton’s sister Archianna to be inscribed in the stone but not Lady Hamilton, it seems of importance that, describing Hamilton’s funeral, Graves wrote that “the grave appropriated to Hamilton, on the north side of the cemetery, is marked by a head-stone, subsequently erected by his family.” That thus seems to have happened not very long after the burial. Archianna Hamilton had died in 1860, five years before Hamilton, and she therefore may have been added to the gravestone while Lady Hamilton was still live, and even though she was not buried there. Was she perhaps added to the stone as a remembrance? And was then an error made, because the inscription suggests her “mortal remains” were buried there? Also strange is that her name was given without date of birth or death, even though Lady Hamilton and her daughter Helen doubtlessly knew these dates.

And if she should have been added only as a remembrance, did perhaps the inscriber of the stone leave too little space to include Lady Hamilton? If that was the case, it may have led Lady Hamilton to decide that she did not want to be inscribed below her sister-in-law and preferred to be seen as one with her husband; she was very pious, and will have taken the biblical unity of marriage very literally, as also her husband did.

I have never seen the last sentence in any photo, ‘Erected by his surviving family,’ which specifically seems to indicate Hamilton. But if that transcription is in order and is at the bottom of the stone, then that would seem to indicate that the various inscriptions were indeed made at different times, with space between them to allow for later inscriptions. Hence giving room for errors.

Why Archianna is on the stone is an intriguing puzzle indeed, and if any one knows something about this, I would love to hear about it.

* The page further shows that in 1867 Archibald, the second son of the Hamiltons, bought the “perpetual right of burial in this plot of ground” for about £8. Further, that in this grave were buried Sir and Lady Hamilton, and their daughter Helen and her husband Archdeacon John O'Regan. In 1900 their son, the Hamilton’s grandson John O'Regan signed the Derivative Assignment Declaration (DA) form. That seems odd, because in 1900 Archibald was still alive: “Where there is no will in existence for the deceased original owner (or surviving spouse) of a grave, then the Mount Jerome DA declaration form applies. ... This DA form may only be signed by the nearest surviving relative (NSR) of the deceased original owner.” In 1920 John O'Regan paid £15, for Care in Perpetuity to this plot by planting Blue & white Violets in Summer & Double white Daisies, ?? in Autumn keeping Stone Clean & reset & Inscription renewed.”

** The transcription often reads “Love is the following of the Law.” Having become curious about such a strange sentence for a grave stone I did a search, assuming that it was, like the earlier sentence, a Bible quotation. It appeared to be from the King James Bible, the letter of Paul to the Romans, chapter 13 verse 10 (left column): “Love worketh no ill to his neighbour, therefore love is the fulfilling of the Law.” The previous sentences in Paul’s letter give the context, “8 Owe no man any thing, but to love one another: for hee that loveth another hath fulfilled the Law. 9 For this, Thou shalt not commit adulterie, Thou shalt not kill, Thou shalt not steale, Thou shalt not beare false witnesse, Thou shalt not covet: and if there be any other commandment, it is briefly comprehended in this saying, namely, Thou shalt love thy neighbour as thyself. 10 Love worketh no ill to his neighbour, therefore love is the fulfilling of the Law.” Therefore, extrapolating very far and without knowing why and when this was added to the grave stone, it might be possible that the family therewith showed that according to them, even though the Hamiltons had an in no way standard Victorian marriage and there was much gossip, their marriage was a good one, and that with their love they fulfilled the Law. But to be very certain this is indeed what is written on the grave stone, I hope that perhaps someone can, some day, make a photo of the grave stone in which the sentence is readable, so we can all become certain about it. And of course of the unknown word before Animae.


Hamilton tombstone at Mount Jerome

These photos have been made by Finbarr Connolly. The tree on the right is standing on the other side of the path the grave is on. It is a beautiful old tree, together with the other trees at Mount Jerome ‘adding greatly to the romance and atmosphere of the cemetery.’



Utrecht, 3 May 2020 — Graves’ opinion about Lady Hamilton, and apparent disagreements

Ever since our gossip article, I wondered when exactly the negative stories about the Hamilton marriage started to become so wide-spread. Usually, local gossip does not completely overshadow someone’s legacy; not many people would have a good public image if the gossip would mostly win from nuanced views. Therefore, every now and then I search for earlier gossip outside Dublin.

Lately, at first to my happiness, I found a book, published in 2012, For Better or For Worse? Collaborative Couples in the Sciences, in which it was noted that in a book by Samuel Smiles, called ‘Character’ and published in or around 1877, Helen Bayly and William Rowan Hamilton were mentioned in a chapter called ‘Companionship in Marriage.’ That could have meant a first glimpse of a positive view on the Hamilton marriage from before Graves’ biography. But having found Smiles’ book on the Internet Archive, it appeared to be about the marriage of Sir William Hamilton of Edinburgh, and therefore alas no ante-biography view on the Hamilton marriage. But very unfortunately, the 2012 authors felt compelled to add a footnote, 52 on p. 53: “Despite Smiles’s inclusions of the Hamiltons, historians noted the strife in their marriage; see Thomas L. Hankins, Sir William Rowan Hamilton (Baltimore, MD: Johns Hopkins University Press, 1984), pp, 114-126.”, and that is of course about Sir William Rowan Hamilton.

The Oxford Dictionary gives as a description for ‘strife’: “Angry or bitter disagreement over fundamental issues; conflict. Australian, New Zealand: Trouble or difficulty of any kind.” Assuming that the word is not used here in the second meaning but in the bitter one, and having read Hankins’ biography, this is certainly not what Hankins wrote. Although he was not very positive about the marriage, he also was not this negative. Hankins did believe that Hamilton only loved Catherine Disney, and that Helen Bayly was no match for both Catherine and Ellen de Vere, the first two women Hamilton had been in love with. Indeed, both Graves and Hankins missed Hamilton’s psychological discovery in 1832, and without it that could be concluded. But as shown in A Victorian Marriage, Hamilton did discover how to handle his melancholy feelings, and thereafter fell in love with Helen Bayly. He clearly and openly loved his wife, and did not in any way see her as less than his former loves.

This is no place to discuss all the pages from Hankins’ biography mentioned in the 2012 footnote, but in A Victorian Marriage I have quoted from each of these pages, 114-126, as can be seen in the footnotes, and placed them in context. The last page, p. 126, contains Hankins’ conclusion about the marriage, that “[Helen] remained the central figure in Hamilton’s life. [...] Hamilton never wrote a word of complaint about his wife.” Which is perhaps not jubilant, but can also hardly be abbreviated to Hankins having “noted the strife in their marriage.”

But one quote is too important to leave unmentioned as it has not yet been discussed here. On the first page given in the 2012 footnote, p. 114 of Hankins’ biography, Hankins gives a letter containing Graves’ opinion about Lady Hamilton, which was indeed extremely harsh. But as has been shown, it was not because she was not a good woman in Graves’ eyes, but because he judged her as weak because she should have “governed” her husband and therewith saved his Dublin reputation. Which is of course a contemplation, not a fact from the marriage itself. Graves also wrote that the Hamiltons “remained attached to each other,” so although he felt compelled to openly judge Lady Hamilton, it was a judgement about the theoretical possibility that things would have been different if she had acted differently, not about what these two people felt for each other. And of course, it can easily be stated that knowing what Hamilton did in his scientific life, it is hardly imaginable how in any scenario he could have done even more.

The letter given by Hankins, in which Graves gave his opinion about Lady Hamilton, was written in 1873, when Graves was preparing the biography of which the first volume was published in 1882, and was directed to Ellen de Vere, then Mrs. O’Brien. In the letter Graves wrote, “After marriage the poverty of her mind and the whole nature must soon have revealed itself to him as not to be ameliorated by all the riches of cultivation which he could bestow upon it.” A very harsh opinion indeed.

Yet Graves’ suggestion about Hamilton’s view on his wife was denied by Aubrey de Vere. In the on this page aforementioned letter he wrote to Graves in 1879, De Vere had written that “up to that time, A.D. 1837, Hamilton’s affection for his Wife had not waned. Indeed I do not know that it ever did [...].” I had not given the rest of De Vere’s sentence because that was not important in that blogpost. But as can be seen here, De Vere’s complete sentence was, “Indeed I do not know that it ever did, or that he ever discovered how little she approached to his early ideal of her.”

Not having seen other letters of the 1879 correspondence between Graves and De Vere, from this sentence it seems very likely that De Vere knew about Graves’ opinion about Lady Hamilton, and this may have been a cautious attempt to contradict Graves. That even if he agreed with Graves that she was not highly learned and literate enough for Hamilton, as they both were, Hamilton himself did not see her at all as they did. And that makes it a question which of these two friends knew Hamilton best. Although that will perhaps never been known for certain, there clearly are arguments to conclude that De Vere knew Hamilton better than Graves did because the friendship between Hamilton and De Vere had been very close, even to the point of spending, throughout the years, many subsequent days with each other, making excursions together, and having had very intense correspondences.

Of course, never discovering that one’s partner does not live up to the early ideal must signify a very happy marriage, and the question thus is where Graves’ harsh opinion came from. During Hamilton’s marriage Graves did not live in Ireland, but every now and then he visited Hamilton at the Observatory, and Hamilton visited him in England a few times. But Graves thus did not really see Hamilton live his daily life; he was received as a guest, and during his stay Hamilton will not have locked up himself to work out some mathematical idea. Graves only came back to Ireland the year before Hamilton died; Hamilton then was very ill already. It thus seems possible, as it has been argued in A Victorian Marriage, that Graves was positive about the marriage until, preparing for the biography, he read Lady Hamillton’s letters.

Having had a goal for the biography, namely counteract the Dublin gossip by showing what a wonderful man Hamilton had been, he then may have judged her, the letters not having been at all learned and metaphysical as he perhaps had hoped, or even had concluded from Hamilton’s positive remarks about the piousness and spirituality of his wife. The letters gave room to the possibility that it had been her weakness which had been the cause for Hamilton’s bad Dublin reputation.

De Vere was not the only one who did not agree completely with Graves’ opinions; after the publication of the first volume brothers of Catherine Disney tried to persuade Graves not to write so openly about events in Hamilton’s personal life. As it seems, they fully understood what could happen when so many people, very near but also far away, would read such emotional stories in such an authoritative biography. And what they feared for indeed happened, Graves’ emotional outpourings now completely define Hamilton’s reputation. But Graves continued to do what he thought he had to do, be honest and mention it all, but conceal the details as well as possible. Which of course even made it worse, because consequently the hints Graves gave to ‘unfortunate circumstances’ were given without detail, leaving them to the imagination of the reader.

Graves obviously hoped that if he would wrap his criticisms in blankets of warmth, people would read his biography as nuanced as he meant it to be. But what people read between the few kind sentences about Lady Hamilton was his very harsh opinion about her. It may be wondered what might have happened if Graves would have had an editor, or had reacted to the remarks from Hamilton’s close friends.

In any case, searching for the start of the spread of the gossip, so far it thus still has to be concluded that it really started with Graves’ biography. That with blaming and denigrating Lady Hamilton Graves achieved the opposite of what he had been aiming for because also Hamilton, as her husband, was therewith regarded a lot less positive. Graves certainly can be felt sorry for, having worked for twenty-five years on his biography, trying to show how wonderful and marvellous his friend had been. A man of extremely high moral standards who, as Graves observed, until the end of his life was “ready to burst out into a genial laugh.” Yet what is left from all Graves’ hard work is a depressed alcoholic in a deranged marriage. If Graves would have known what has been concluded from his biography, he would have turned in his grave.



Utrecht, 25 April 2020 — Lady Helen Hamilton’s crushed reputation

Having published about the private life of the Hamiltons, and thereafter about Catherine Disney, I realised that almost everything I wrote about Lady Hamilton was derived from what others wrote about her. Unfortunately, that also holds for Catherine Disney, but as far as I know the only example of her handwriting is the shaky and smeared out signature on her marriage record, looking very sad and perhaps desperate indeed. I have never heard about still extant letters written by her. That is different for Lady Hamilton; letters by her are kept in the Trinity College Dublin Library.

Still, in their respective biographies both Graves and Hankins only gave a few sentences from Lady Hamilton’s letters, which made us very curious about the rest of what she wrote. We therefore visited Trinity Library last summer, and saw the majority of her letters. Her correspondence is indeed not very extensive as Hankins already remarked in his biography, but they certainly show a glimpse of who she was which is in itself interesting, she was after all the wife of a famous genius, who worked very hard, and mostly at home.

I am now preparing a third book, about Lady Hamilton’s correspondence. The reason I want to do that is because of the extremely negative view on Helen Bayly, later Lady Hamilton, which is nowadays even far more negative than the view on Hamilton himself. That started in the 1880s, when Graves wrote his biography about Hamilton, and blamed Helen Bayly for Hamilton’s bad Dublin reputation. She had already been gossiped about in Dublin, just as people gossiped about Hamilton, yet the wide-spread view on Helen Bayly as an overall “weak wife” originated in the biography.

Hamilton has been described as an overeating alcoholic, and the deterioration of his reputation is still going on, yet about his character everyone has remained to be positive. But Helen Bayly has been sacrificed on the altar of Science; to save Hamilton’s reputation, hers was damaged beyond recognition. Graves firmly believed that it was her ‘weakness’ which prevented her to stop Hamilton from drinking; he does not even seem to have considered for one moment that, like Hamilton, she just did not have a problem with it. Still, he otherwise did not write negatively about her as a person; he called her an “attached wife” and a “good woman,” who “won the good opinion of [Hamilton’s] friends,” and he never claimed that the marriage was unhappy, even on the contrary. But the emotional tone with which Graves put the blame about Hamilton’s Dublin reputation on her dripped into everything that was written about her afterwards.

The blame Graves laid upon her led to what comes close to character assassination. Completely ignoring the positive remarks Graves made about Helen Bayly, and ever further extending his negative remarks, she has been described as having been a “pathologically shy and timid” “semi-invalid” “hypochondriac,” a “local lass” from “across the fields from the observatory,” a “country preacher’s daughter” who “absented herself for long periods of time.” She is said to have been “mentally limited” and ‘unable to look after the children,’ a “frustrated young girl” [jeune fille frustre] with “neurotic and probably slovenly tendencies”, “a totally disorganized woman” [une femme totalement désorganisée] who was “unable to provide an orderly domestic regime” causing her husband to live in “squalor.” Sometimes an attempt at kindness is made, that she could be ‘pitied’ for “having to stand by and watch her husband have his self-absorbed ‘moment of genius’,” i.e., finding the quaternions.

It is of course not known for certain how she felt when Hamilton found the quaternions, but from what is known about them she will have been very proud, having been present while her beloved husband found such a delightful solution for the problem he was working on, which had occupied him so much that in the two weeks prior to the discovery they had asked him at every breakfast if he could multiply triplets already. It must have been wonderful to watch him scratch the formulae on ‘Brougham Bridge’ out of pure happiness.

Reading Graves’ biography, and the letters by Hamilton given in it, it is indeed obvious that the ‘facts’ about Lady Hamilton as quoted above do not fit Hamilton’s remarks about his wife at all. And using our ‘gossip article,’ the sources of these claims can be traced back to their origins, the contemporary gossip apparently having started in the early twentieth century.

Last summer, when we were in Dublin, we saw Lady Hamilton’s letters, and I am slowly transcribing them. Helen Bayly clearly did not like writing letters, and indeed did not write many; she only did it because Hamilton liked receiving letters from her. All that is left of people from those times are letters and notes, hence there is not much which can be used to easily disclaim everything which has been written about her. Yet there is enough to show a very different woman than how she is depicted in the gossip.

What I have read in her letters until now completely fits the picture of her as it emerged from Hamilton’s letters and some remarks made about her by Graves, Hamilton’s Uncle James, and her granddaughter-in-law. Combining them all, Helen Bayly was regarded as an “amiable wife” of “lady-like appearance,” who apparently was truthful and direct, used to speaking her mind, sometimes grumpy and able to get angry, proud of her family and her husband, funny and amused, fashionable while seemingly able to understand (some?) technics. She read and talked about poetry, in any case Shakespeare, Chaucer and “poets of lore,” and the poetry of her husband and of her sister-in-law Eliza Mary Hamilton. Helen Bayly did have a weak health but she certainly was not always ill; she rode a horse, and in later years had her own ‘Arabian’. She made “her own independent excursions” and frequently visited, and was visited by, members of family from both Hamilton’s side and her own. And not the least, she provided a household which made it possible for her husband to do all the work he became so famous for.

Preparing for the book about her, perhaps consisting of annotated letters, it will take a long time to finish because we have to go back to Dublin, which this summer will be impossible due to the corona virus. We have, for instance, to visit Bloomfield in Donnybrook where Lady Hamilton died, and see her original letters in Trinity College Library; due to a miscommunication, of most letters we saw only the xerox copies, which are not good enough for a complete transcription. I therefore decided to already give interesting facts here when I encounter them.

The first one, which then immediately disproves the idea that Helen Bayly was some unfortunate local girl, as I indeed also had concluded from pieces on the internet before starting to read Graves’ biography, is Lady Hamilton’s descent. It has been claimed that she was no match for Hamilton’s earlier two loves, Catherine Disney and Ellen de Vere, who came from important and rich families. Yet next to Helen Bayly’s father having been rector of Nenagh and Knigh, and curate of Kilkeary, Dromineer and Ballinaclough, the Baylys were a large, prosperous and influential land-owning family* in Tipperary, the “main landlords of Ballinaclough in the 19th century. Unlike the national stereotype of the time of landlords being part of an elitist landed gentry, the Bayly’s were known in Ballinaclough as good and fair landlords. They were considered to be the poor man’s friend.”

This sounds like a kind and attached family and indeed, within the Bayly family many members seem to have had close ties. Helen Bayly was an openly beloved daughter, sister and relative; that was the woman Hamilton fell in love with.

* Being Dutch myself, it often feels strange to almost brag about families of the landed gentry in Ireland in the Ascendancy, just like it would about Dutch influential families during the colonialization of Indonesia. Yet Hamilton was a member of the Ascendancy, and this is about those families themselves. I found a for me very enlightening blog post of the Silvermines Historical Society, about the “Buck Gate” of Kilboy House where the Prittie family lived, who were directly related to the Baylys. It describes the history of the house from the perspective of the children who “grew up around Dolla and Silvermines in the [nineteen] fifties,” and greatly helped me to place some things into perspective. It can be read here, Beyond the Buck Gate.



Utrecht, 24 November 2019 — Hamilton’s intellect, Grace McFerrand, and why Archibald Hamilton did not attend College

It has often been stated that Hamilton’s intellect must have come from his mother. One reason for that assumption is that in 1866 Peter Guthrie Tait (1831-1901) claimed* that Hamilton’s mother Sarah Hutton had been a relative of the mathematician Charles Hutton (1737-1823).** Yet Graves showed that Sarah Hutton was not related to the mathematician.

Note added 2021: The notion that with writing “Dr. Hutton” Tait meant the mathematician Charles Hutton may have been a result of assumptions and interpretations. In giving his first name, Charles, Graves adds “presumably,” yet that has been lost in history. It is indeed far more likely that Tait was writing about James Hutton, the Edinburgh geologist.

Another reason is that Hamilton’s father Archibald did not go to University. That seemed to signify that he was less intelligent than his brother James, the uncle in Trim who educated Hamilton, and who was a graduate of Trinity College Dublin, even a premium man. There is much reason to doubt this assumption however; although Graves criticised Archibald’s letters because in his eyes they were not learned enough, he was clearly very positive about Archibald,*** making the idea that Archibald would have failed University very illogical. The question thus was why he was not sent to college. It appeared to be a question of money, that is, a lack of it.

Archibald Hamilton’s mother, Grace McFerrand (1743- ca 1808), entered the family through a “romantic incident;” when she was about fifteen years old a shipwreck took place near Kirkmaiden, where she lived with her family. Mr. and Mrs. Hamilton of Killileagh Castle were amongst the shipwrecked, and they stayed in the McFerrand home for three weeks. They became attached to the family and especially to Grace, and they asked the McFerrands if they could adopt her. Her father refused, “partly from a delicate feeling of independence, partly because he desired himself to educate a child of great promise.” But after his death in 1763 her mother was in financial trouble; in those days women were almost completely dependent of the men around them. She asked the Hamiltons to take Grace in, and so, when Grace was twenty or in her early twenties, she came to live at Killileagh Castle.

At some time, it is not known when, she was introduced to William Hamilton, an “eminent apothecary,” working at 30 Jervis street in Dublin; Grace would marry him in 1774, eleven years after the death of her father. That means that, although it is not exactly known when she came to Ireland, she must have lived at Killileagh Castle for quite some time.****

Uncle James was born in 1776 and Archibald in 1778; they thus both were still very young when in 1783 their father William Hamilton died. Having been an apothecary, it can be assumed that he earned a very decent income. But in those years women who lost their husbands often also lost large parts of their social status, and if they did not have an inheritance to live from or family members who could help out, they had to work very hard while earning less than men.

After the death of her husband, for some time Grace’s brother-in-law Roger Hamilton ran the apothecary, but in any case before 1791, when her son James entered college, he must have died. In 1791 Grace Hamilton McFerrand is listed at 30 Jervis street as a haberdasher, which in England is someone who sells necessities for sewing, such as sewing thread and needles. It will have been impossible for her to have two sons attending college. Although Mrs. Hamilton of Killileagh Castle offered financial help she refused, and apprenticed Archibald to an attorney.

That Archibald Hamilton did not go to University thus had nothing to do with not having been intelligent enough and indeed, according to Graves Hamilton’s intellect came from the Hamiltons instead of from the Huttons, even though they were an “intellectual family.” That is of course as unnuanced as claiming the Huttons as the source of Hamilton’s intellect; they knew nothing about genetics, and even knowing about that now it is not known how such amazing intellects come into being.

Still, in every generation there seem to be some such extreme prodigies, and it must be very difficult to raise such children and protect them from vanity. Hamilton was lucky; his family was very aware of these dangers and warned him from a very young age. Yet even then Hamilton had to work on his humility all his life, and it is to be hoped that the contemporary prodigies are guided and protected from vanity as thoroughly as Hamilton was.

* In his 1866 article, Tait had also claimed that Hamilton’s “grandfather came over from Scotland to Dublin with two young sons,” signifying James and Archibald. This statement is also incorrect; it is for instance known that the eldest brother was Arthur, who was born in Jervis street. Yet it has also often been repeated, for instance volume 24 of the Dictionary of National Biography, 1885-1900.

** Coincidence or not, Charles Hutton used the word quaternion before Hamilton did; he appears in the 1762 - 1849 time frame of Google’s Ngram Viewer. The word quaternion was used in the King James Bible, of which it is certain also Hamilton owned a copy. It is found in Acts 12, 4, foure quaternions of soldiers.

*** Graves wrote, “Archibald Hamilton [...] was a man of great energy and strong impulses, of remarkable business powers, of exuberant eloquence, both of the pen and lips, of strict evangelical views of religion, and of zeal in expounding and enforcing them, but withal of tender affections, and a convivial disposition; delighting in repartee, whether his own or that of others, and much given to quizzing (as then the phrase went) some companion or fellow-traveller, a tendency, however, which was kept in check by his strong practical sense and sound moral principles.”

**** Although Hamilton’s father Archibald Hamilton claimed that his name came from Archibald Hamilton Rowan and that doubtlessy will be true, also Grace’ maternal grandfather, who came from Edinburgh, was called Archibald.



Utrecht, 11 November 2019 — A terrible hailstorm in 1850, and Biela’s comet

Since early November, Finbarr Connolly has been providing me with much very interesting information. Most of it will find a natural place within the various subjects, but others are to good not to write something separately about them.

For instance, a newspaper article Finbarr had found, which mentioned a terrible hailstorm in Dublin on 18 April 1850. The article is from the Nenagh Guardian, and it describes how hail stones as large as musket balls caused very much damage in large parts of Dublin. Searching in Graves’ biography, he indeed also wrote about the storm; I had completely forgotten about it.

Graves wrote, “The Observatory came in for its share in the effects of the remarkable tornado, described fully by Dr. Lloyd in the Proceedings of the Royal Irish Academy, which visited Dublin and its neighbourhood on the 18th of April in this year. I find the following record of it in a note of Hamilton’s: “We had an awful storm of hail and thunder here about the middle of yesterday. Our sky-light was dashed to pieces, and the rain is at this moment pouring in. I was at work myself for hours upon the roof of the house after the storm subsided, together with a workman and my son Archibald, directing and assisting in the removal of the masses of hailstones that had fallen, and which (it seemed possible) might have injured the slates or the lead. In Dublin I am told the damage done is terrible, and where a glazier can be caught, I am sure that I do not know.” [Graves 1885, 649-650].

In 2017 coincidentally having reread this page in Hamilton’s biography had led me to write my fireball article, because immediately after the foregoing quote about the storm Graves wrote in a loose, inconspicuous sentence, that “not long after this, [Hamilton] sent to the Saunders’ Newsletter a very full account of a beautiful meteor, seen by him on the night of the 13th of May, as he was walking home from the meeting of the Academy.”

But then Finbarr mentioned that he had found the description of the consequences of the storm at Dunsink in an article written bij by F.E. Dixon in 1950, about Dunsink Observatory (unfortunately not open access). Reading the article I suddenly saw that, very remarkably, Dixon did something similar as Graves had done when he wrote, almost out of nowhere, “Only once did [Hamilton] dabble in “popular” science — when he contributed two short articles on Comets to the Dublin Penny Journal.” These articles, about Biela’s comet, would hardly have been found in a different way because Hamilton did not use his name in the article, he just signed with ‘H.’

Being very happy with Dixon’s remark, I searched for Hamilton’s articles, and fortunately, all four volumes of the Dublin Penny Journal are open access available. I then copied, for better readability, or findability, Hamilton’s article and wrote an introduction, Biela’s Comet. And promptly found that it had been copied already, The Mathematical Papers of Sir William Rowan Hamilton: Volume 4, Geometry, Analysis, Astronomy, Probability and Finite Differences, Miscellaneous, edited by Brendan Scaife. Well, in any case, there it did not have an introduction.



Utrecht, 23 October 2019 — Dunsink Observatory, the Meridian room, and again Hamilton’s birth house

Erroneous information can lead to extraordinary events. When we were in Dublin this summer, we had some days between the Maynooth conference and the reopening of Trinity Library on 6 August. We decided to search on the internet if it would be possible to visit Dunsink Observatory, and to our happiness, the infobox next to the results of the Google search for Dunsink Observatory showed that the Observatory was open on Sunday, 9am-5pm. We immediately decided to visit the observatory then.

Sunday was an extremely hot day, but we went by train to Navan Road Parkway and walked uphill to Dunsink, needing quite a few heat breaks. Having arrived at the gate, we were very disappointed; it was closed. Much in doubt what to do someone walked past us and suggested to call the observatory, which we did. To my surprise the telephone was answered by a woman called Hilary, and when I told her that I had written about Hamilton, she offered to receive us at the observatory on Wednesday. We did not have to think twice about that, and happily accepted.

When we arrived at Navan Road on Wednesday, Hilary O’Donnell picked us up from the station and drove us to the observatory where we had some amazing hours with her. Hilary showed us the rooms on the first floor of the Observatory, unfortunately we were not allowed to go upstairs. She showed Wayman’s working room, the kitchen (where she made us coffee and tea), the Meridian Room, and the room which is going to be the ‘Hamilton room’.

In his Dunsink Observatory-Outbreak of Fire, Patrick Wayman wrote that in 1974 the Meridian Room had been reconstructed, and that in 1977 it was destroyed by a fire which had started in the basement beneath the Meridian Room. In the article Wayman wrote that the “intriguing roof structure” with the “sturdy queen-post beams”, and the “cast-iron stays and wheeled runners” of the original shuttering, had been badly damaged. Although changes had to be made in the arrangement of the Meridian Room, the shutters have been reconstructed (but not opened), and the original appearance restored. Hilary told us that where possible the iron work for the roof was reused, and a few elements of it can be seen at the top in Eli’s right photo.

I was happy to be in the Meridian Room again; we were there in 2015, and although not the same as in Hamilton’s time, when I wrote the article about the 1850 fireball, that had helped greatly to imagine how Hamilton’s son William Edwin had seen the meteor from the Meridian Room. But in 2015 I had not paid much attention to details, certainly not to where the transit telescope would have been; I then had not found Hamilton’s report about the meteor yet.

Upon arrival I had told Hilary about Hamilton’s meteor, and in the Meridian Room she asked me where I would think the telescope had been. Normally I am very bad at knowing directions without seeing the sun or moon, but writing the article I had imagined looking through William Edwin’s eyes while he was sitting in the transit chair, and therefore I knew where that was while being inside in the Meridian Room. Hamilton had written that the window William Edwin saw the meteor through had been, “although facing the south, [...] distant by several feet towards the west from the large slit in the roof to which the transit instrument was directed,” so the slit must have been somewhere near the entrance to the Meridian Room. I think there now are two slits in the roof, one where we are in the photos and one at the opposite side, and when I answered her that it must have been the one which can be seen on the photos, she agreed. If I remember correctly, she told us that they indeed had found traces of the telescope, or its mounting, beneath the floor.


Hilary and Anne in Dunsink’s Meridian Room

Hilary and Anne talking in Dunsink’s Meridian Room about the path of the 1850 fireball, and how Hamilton measured its trajectory. Hamilton had seen the meteor when he was outside, William Edwin saw it while sitting in the transit chair, which must have been at about the place where we are in the photos.
Updated 16 October 2020: to my surprise, as can be seen in the video of today’s virtual Hamilton Walk at around 6 min into the video, the meridian telescope was at the next shutter, further in the room. In 2019 we had not seen the meridian pillars outside!


In the Hamilton room Hilary told us about her work at the DIAS-ESTEC experiment on the LDEF, the Long Duration Exposure Facility, which had been brought into orbit in 1984 and was, due to the terrible accident with the Challenger in 1986, only retreived again in 1990, yet therefore containing very much data. And about how unusual it was for women then, and even now, to work in technology and engineering. When she thereafter showed us Wayman’s working room we saw a photo of Hilary, Emer Kee and Dinah Molloy, part of a series of photos such as this one, made at the celebration of the recognition for their work by the Dublin Institute for Advanced Studies, DIAS, and by the minister for higher education Mary Mitchell O’Connor.

And to our amazement, in the Hamilton room we saw the tablet which had been on Hamilton’s birth house in Dominick street! We had searched in vain for the house in 2015, and then having traced it quite easily online, in 2019 it had been very easy to find it; we even stayed in Dorset Street almost around the corner. How the tablet ended up at Dunsink we do not know, perhaps someone thought that after so many years it would be a good idea that they should have it.


Tablet on the wall of Dominick Street in 1907

The tablet which in any case had been on the wall of Hamilton’s birth house in The Story of Dublin (1907).


The left and right Google street view image show the block of six houses in Lower Dominick Street where Hamilton was born. As seen in the left image, the houses are numbered from right to left 33 to 38, and Hamilton was born in what is now no 36. Someone in Dublin had told us that the front of the block had been preserved, but that the inside had been completely renewed. That can indeed clearly be seen in the image on the right; the Georgian chimneys which still are on the other houses are not on Hamilton’s block any more. But on the image in the middle it can be seen that also the front of the first floor has been replaced with concrete, which may have been the reason the tablet was taken off.


Dominick Street

Hamilton’s birth house was in what is now 33/38 Lower Dominick Street, Bolton Square, apartments 21-40. On the left and the right Google street image the block of six houses can be seen; that block is Lower Dominick Street, from right to left no 33 to 38. Hamilton’s birth house is indicated by the ten windows of no 36, at the left side of the dark front door in the middle image. In this pdf we described the online search after the precise location of the house. The link to the “regeneration plan”* in the pdf is not active any more, the plan can now be found here. See also the Dublin City Architects Blog.


* It is good to read that residents of the flats complex, which was built in 1961, won their decade long fight for a refurbishment of the flats. Our own appartment buildings, built in 1969, were also destined to be demolished, and it took years and, unfortunately, the financial crisis, to save them. So we do understand how difficult it must have been.


Moving house in 1818

Not often mentioned is that early in 1818 Hamilton’s father Archibald Hamilton moved to 18 Dominick Street; Graves’ biography mentions one letter Archibald Hamilton wrote on 20 May 1819, while living at no 18 [Graves 1882, 57].

The houses in Dominick Street were renumbered after 1818 when Archibald Hamilton moved house, and before 1852 when Hamilton wrote to De Morgan that his birth house had been no 29, and was now no 36 [Graves 1882, 53]. The church at the opposite side of the street was built later; “the Dominican Priory of St. Saviour’s in Dublin was first founded in 1224 on the site today occupied by the Four Courts. The present church was designed by J.J. McCarthy and opened in 1862.” The church can be seen in the left and right photo above.

The number of Hamilton’s birth house having been changed from 29 to 36, at the renumeration no 18 may have become no 25. If that is the case the house will unfortunately have been demolished when the church was built because the house next to the church is no 24.


Added later: The twentieth century history of the house

Finbarr Connolly (see 11 November 2019) sent me three newspaper clippings about Dominick Street. One is from the Dublin Evening Herald of 8 May 1965, a short article called ‘Historic Dublin Street’,* about Lower or Old Dominick Street. It mentions that “in the house, now No. 36, a few doors from Bolton Street, the famous mathematician, Sir William Rowan Hamilton, was born.”

* In this short article it is also mentioned that “Two members of the United Irish Society of very opposite character lived on opposite sides of this street. The house, No. 1, at the corner of Great Britain Street [now Parnell Street], was the residence of the honest and honourable Archibald Hamilton Rowan, whose name is associated with the history of Clongoes Wood College.” According to Don Gifford, in Joyce Annotated, “Rowan was convicted of “seditous conspiracy” in 1794 but escaped from the British troops escorting him to prison and took refuge at Clongowes Wood Castle. Just as he closed the library door, the troops are supposed to have opened fire. He then is supposed to have thrown his hat onto the “ha-ha” from the library window to give the impression that he had leapt from the window and escaped; meanwhile he hid in a secret room until he could be smuggled away to France. He was subsequently pardoned and allowed to return. A ha-ha is a bank or dry moat designed to keep cattle off the lawns and gardens around a house without obstructing the view. The story of the escape may very well be schoolboy apocrypha, though Rowan did get away to France after his conviction.” The short article ‘Historic Dublin Street’ continues, “In a house in Dominick Street nearly opposite lived the now notorious Leonard McNally,whose dishonour was never discovered until after his death in 1820.” McNally had been a barrister, who was influential in the development of the “beyond reasonable doubt” standard in criminal trials. He also was a founding member of the United Irishmen. Yet while defending many of the leading members, such as Robert Emmet and Lord Edward FitzGerald, the father of Hamilton’s friend Lady Campbell, he secretly worked with the British to have them convicted.


The other two newspaper clippings Finbarr sent me show that the tablet was on Hamilton’s birth house in 1938 and 1964, and I then found yet another one, from 1952 or 1953. The tablet as shown in the left and middle picture can easily be recognized as the one which now is at Dunsink, shown above.


Dominick Street

The clippings answer most of our questions. Although we still did not find when exactly it was decided to honour Hamilton with this tablet, it was on the wall next to the front door of no. 36 in any case from 1907 until 1964 (each of the six houses in the block still had its own front door). Someone had told us that the house had been demolished and in a sense that is true; in the middle picture, showing the front door in 1952 or 1953, it can be seen that the house was indeed in great decay, and around the 1960s it was apparently decided something had to be done. In or before 1964 the “top portion and rear of the house down to first floor level” was demolished, but not the wall containing the tablet.

The neighbouring houses, nrs. 39 to 43, and the houses on the opposite side of the street from the church up to nr. 20, are still more or less the original ones, which can for instance be recognized from the Georgian style chimneys. Noticing that they slightly differ from each other but are all four storey houses,** it can also be concluded from the 1964 clipping that Hamilton’s birth house originally had four storeys, instead of assuming, as I had done at first, that it was a five storey house of which the ground floor and the first floor had been spared. One of the reasons I had assumed that the walls of two storeys had been spared, and therefore the house had been a five storey building all along, was the fact that the wall to which the tablet was attached had not been included in the demolition although the tablet was very close to the window of the first floor.

** On the left side of the left photo above, it can just be seen that the original Georgian houses had large windows downstairs, and smaller on the higher storeys, the smallest windows on the top storey. Someone in Dublin, we unortunately forgot who, told us that in those days people had to pay taxes for light in the house. The larger the windows, the higher the taxes. So the storeys where the servants and the children slept, had smaller windows than the lower storeys where the owners lived and guests were received. Also, having more than ten windows in a building was taxable, and that is why many large buildings are still seen in Dublin to have (part of their) windows bricked up.


So, in 1964 just the front wall of the ground floor was still original, but at some time it was decided to change the front doors and make three common entrances for the six houses. We could not find when that happened, but it must have been done before the trees were planted which can be seen in this early 2018 photo from MyHome.ie. Such a renovation would be difficult with trees so close-by, so they will have been planted after the last renovation. The trees have now been sawn off as can be seen in this September 2019 Google Street view recording.

In any case, that last renovation apparently was the end of the tablet on the wall, and now the interesting question arises whether this is still Hamilton’s birth house, if not any part is original any more. It could be argued that it does not deserve a tablet, because it is a different house. On the other hand, it was never completely gone, and looking at the brick walls of the higher storeys and comparing them with the wall of no 39 which still is orginal, hardly any difference can be seen. So unless one is an architect, or a historian, only the front doors and the concrete ground floor wall betray its not being original.

There thus is a house, looking very much like the original, and standing on the same foundations; we think that should be enough to give it a nice new tablet.


If there is information I missed, such as for instance that contrary to what I now think after 1964 the whole block was demolished and rebuilt, or if you know how the tablet ended up at Dunsink, please contact me.



Utrecht, 19 October 2019 — Lady Hamilton’s last years, a pension and Allendale Cottage in Drumcondra

Updated September 2021

When we were in Dublin we saw some of the very many letters and papers in the Hamilton collection in Trinity College Library, and I will, every now and then, add information here about what we read. This is about two drafts for the same letter; a thank you letter from Lady Hamilton and her daughter Helen Eliza Amelia to Lord Wodehouse, shown below. The first one is from photos we took from the original letter, the other of photos we took from xerox copies. We had mistakenly indicated that we wanted to see these copies, instead of the real scans.

After Hamilton’s death in 1865 Lady Hamilton, William Edwin and Helen Eliza had to leave the observatory; in any case from 1864 until 1868 Archibald lived in Clogher. That they had to move out is in itself logical, Hamilton’s successor as Royal Astronomer had to move in, but the Hamilton family had to move house while they were mourning the loss of their beloved husband and father. Where grown up children mostly leave the house of their parents eventually, for Lady Hamilton it must have been very difficult. Just because her husband died she had to leave the house she had called home for such a long time, where she had lived an intense life having taken care of that hard working and very famous man, and where her children were born in; married women in those times owned nothing. After the deaths of their husbands women often became completely dependent on the men around them, who could help them or ignore them, in which latter case every comfort they had would simply cease to exist. Of course, after the deaths of the men around them many women then were in far more destitute circumstances than Lady Hamilton was, when she died four years later she still had £1500, about twice Hamilton’s yearly income. Nevertheless, she did not know of course how long she would live, and she may have stressed about whether that amount would be enough to live from in case she would live unto her 75th year, as for instance her mother did. Fears of becoming old and poor, certainly if her ailments would become worse, must have been terrible, and in both drafts shown below it can be read how relieved she was knowing she would receive an income until the end of her life because the Lord Lieutenant granted her and her daughter Hamilton’s 1842 pension of £200,* to be equally divided between them.

* This was quite a substantial amount of money then. According to the website MeasuringWorth, “In 2019, the relative value of £100 from 1865 ranges from £9,632.00 to £231,400.00. A simple Purchasing Power Calculator would say the relative value is £9,632.00. This answer is obtained by multiplying £100.00 by the percentage increase in the RPI [Retail Price Index] from 1865 to 2019. This may not be the best answer. If you want to compare the value of a £100 Income or Wealth in 1865 there are four choices. In 2019 the relative: — real wage or real wealth value of that income or wealth is £9,632.00, — labour earnings of that income or wealth is £69,730.00, — relative income value of that income or wealth is £89,040.00, — relative output value of that income or wealth is £231,400.00.” See the MeasuringWorth website for background information.




Draft of a letter from Allendale Cottage, written by William Edwin Hamilton



Lady Hamilton, first page of a draft of a letter from Allendale Cottage              Lady Hamilton, second page of a draft of a letter from Allendale Cottage



The first draft is in the handwriting of the Hamilton’s eldest son William Edwin; Lady Hamilton will have been practising the letter with him. After the family had left the Observatory, William Edwin may have lived with his mother during the months they had to sort out Hamilton’s papers, and he was preparing the publication of the Elements of Quaternions. William Edwin dated the foreword “January 1st, 1866,” only two days after the date on the draft. Soon thereafter he left for Canada, making his “seventh and last trip from Glasgow to Quebec in spring of ’72.”


Allendale Cottage Drumcondra Cottage near Dublin Dec 30/65.

My Lord

My daughter and I respectfully request your Excellency to convey to Her Majesty an expression of our deep sense of Her Majesty’s goodness to us as shown by her gracious intention to confer upon us a pension equal in amount to that enjoyed by my late husband.
Permit us also, to thank your Excellency most warmly
Our most grateful thanks are also due to Earl Russel for his goodness in recommending my memorial to the favorable consideration of her Majesty.
Permit us also to thank your Excellency most warmly for the effectual advocacy with which you have supported it, and which has resulted in placing us in a position of comfort we could not otherwise have hoped for.

I have the honour to remain your Excellency’s obedient servant,
Helena Maria Hamilton.

To his Excellency The Baron Wodehouse, Lord Lieutenant of Ireland.
A note is added, apparently in Lady Hamilton’s handwriting, “Letter to W.h. contains your offer this Evg.”

Having seen her letters in Trinity College Library, this second draft was easily recognized as being in Lady Hamilton’s handwriting.

draft

My Lord,

I write in the name both of myself and my daughter respectfully to request your Excellency to convey to Her Majesty the Queen the expression of our deep sense of Her Majesty’s goodness in conferring upon us a pension equal in amount to that which had been awarded to my lamented husband.
Our most grateful thanks are also due to Earl Russell for his kindness in recommending my memorial to the favourable consideration of her Majesty.
Permit me also in conclusion to tender express to your Excellency our warm gratitude for the interest which you have manifested in our case & for your efficient advocacy of my memorial, to the success of which we owe a prospect of comfort & happiness in this life which we could not otherwise have expected.

I have the honour to be, my Lord, your obliged humble servant. H.

outside
To his Excellency The Baron Wodehouse, Lord Lieutenant of Ireland, Vice Regal Lodge, Phoenix Park.


In the first version her address is given: Allendale Cottage, Drumcondra. Curious about where Allendale Cottage was I started a search, and found that according to the Dublin Street Directory of 1910 a certain James Hennessy lived in Richmond Road in Allendale Cottage, and that in the Electoral Rolls of 1910 his address was given as 79 Richmond Road. That the Street Directory page really is about Richmond Road can be seen by further comparison, for instance, in both documents it can be seen that James King lived at no 31, James M’Grath at no 101, and Mrs. Maria McGrane at Gracepark House. Not all names are the same, perhaps these people did live there, but the voters may not always have been the same people as the people whose names were given in the Street Directory. Still, Hennessy having been mentioned in both lists I think it can safely be assumed that Allendale Cottage was Richmond Road no 79.

Searching with Google maps, I found that coming from the side of the lower numbers after Richmond Road 77 there are no houses any more, there is the Drumcondra Football club, and then on the corner with Gracepark Road is Gracepark House. That house has no number on it, but it is presumably no 93 because the next house is no 95. In the Electoral Rolls of 1908 there is mention of a Kate Gumbrielle who lived at 81-89 Clifton Cottage; no 91 is not in any of the lists. I would therefore assume that no 91 was demolished before 1908, Allendale Cottage (79) at some time after 1915, and Clifton Cottage (81-89) perhaps at the same time as Allendale Cottage, but after 1923. That year Clifton Cottage still existed; it was mentioned as someone’s address in proceedings of the Institute of Chemistry. That is not open access, but a Google search for “Clifton Cottage” “Walsh, Patrick Michael” gives the 1923 hit.

Lady Hamilton thus spent her last years in Drumcondra, and she seems to have lost her eyesight before she died on 2 June 1869, four years after her husband. It has been stated that she spent these years in complete seclusion but that seems again exaggerated, as many statements about her are. Archibald had invited her to come and live with him and Helen Eliza in Clogher but she refused; it can be assumed that losing her eyesight she did not want to leave Dublin any more. Her friends and family were there, and presumably the doctors she was used to most of her adult life. William Edwin was in Canada, but there is no reason to assume that Helen Eliza or Archibald did not visit her. Or her, according to Graves, “always attentive and attached” nephews and nieces from Scripplestown and Dunsinea, who had been neighbours when she lived at the observatory. Or even members of her family-in-law. Also close friends of Hamilton may have talked with her or even visited her; Clement Mansfield Ingleby, who in 1861 had visited the observatory for the first time [Graves 1889, 135, 172], wrote, four years after Hamilton’s death and remarking that his wife “survives him,” that “there is a daguerreotype of Sir William, and his lady and family, in the possession of his widow,” something he obviously would not have known if she never talked to anyone.


Allendale Cottage

Having found that Allendale Cottage, where Lady Hamilton lived in any case in December 1865, will have been 79 Richmond Road in Drumcondra, it would be great to be as certain as possible. And still not knowing where her grave is, perhaps this could also help find it.* The three questions still open are:
— Is it true that these houses were demolished, and if yes, when?
— Does any further information about Allendale Cottage exists?
— The address of Drumcondra AFC is given as 157 Richmond Road even though it is next to no 77, and there also is a 157 Richmond Road, where for instance the Troubadour Rehearsal Studios are, and which indeed is next to no 155. What is the difference between these two no’s 157? And could that influence my suggestions about Allendale Cottage having been demolished?

I would very much appreciate any help in this. If any one has information, please contact me.

* Note added August 2020: It was a relief to find that Lady Hamilton was buried at Mount Jerome with her husband, see Lady Hamilton’s grave. The search for her burial place was reinforced by finding an advertisement, placed in July 1869 in Saunder’s Newsletter, “We are requested to state that Mr. W. E. Hamilton, eldest son of the late Sir William Hamilton, was prevented, by absence the province of Quebec, Canada, from attending the funeral of the late Lady Hamilton, last month, at Mount Jerome Cemetery.”


Addition to Lady Hamilton’s Drumcondra address, and her place of death

Early in November 2019 I was contacted by Finbarr Connolly, who provided much extra information. He had found Lady Hamilton’s entry in The National Archives of Ireland, in the Calendars of Wills and Administrations, 1858 - 1922. The entry states that Lady Hamilton died on 3 June 1869 instead of 2 June, as was given in the advertisements.* Yet the advertisements might be right; having been buried on 5 June would indeed rather indicate 2 June. Interesting is that the entry in the Calendars further states that she had lived in “Allendale Fairview Drumcondra.” Searching if that address would change anything that was fortunately not the case, but I did find, on the website of the Dictionary of Irish Architects 1720 - 1940, that from 1865 until 1877 the “architect and builder of Drumcondra,” Henry Allen, also had lived there, which means that Lady Hamilton may have been his tenant. That would not be unusual; in the Electoral Rolls it was seen that in the early twentieth century many house owners there had tenants, and that may also have been the case already in the 1860s.

* There were quite some advertisements relating her death, for instance in the Cork Constitution: “7 Jun 1869, 2nd inst., Lady Hamilton, widow of Sir William Rowan Hamilton, LL.D. Royal Astronomer of Ireland.” Or the “ Downpatrick Recorder, Down, Northern Ireland: June 2. Lady Hamilton, relict of Sir William Hamilton, LL.D.. Royal Astronomer of Ireland.”

Surprisingly, the entry also gives her place of death: “Bloomfield, Donnybrook.” Bloomfield House was a Quaker hospital, founded by the Society of Friends. The hospital, then called ‘Bloomfield Retreat’, opened on 16 March 1812, and was what then was called a ‘lunatic asylum’, yet patients were admitted there voluntarily. Moreover, Bloomfield Retreat was a relatively small asylum; around the time Lady Hamilton was there, there were only about forty patients. The hospital still exists, but was moved to Rathfarnham.

Having read about general Victorian lunatic asylums, while writing A Victorian Marriage I had a very negative view on them, but apparently, already many years before Lady Hamilton was admitted to Bloomfield, taking care of people who were ‘mentally ill’ had been changing; Arthur Williamson writes, in his The Beginnings of State Care for the Mentally Ill in Ireland, “The period 1805-17 saw a rapidly rising tide of interest in lunacy reform in the British Isles. The illness of George III caused widespread discussion. Quaker experiments in treatment gave new hope.”

In her open access available The Cost of Insanity in Nineteenth-Century Ireland, Alice Mauger compares a variety of asylums, one of them being Bloomfield Retreat. In the Introduction she paints a more nuanced picture of the treatments in the nineteenth century, arguing that for the poor the changes did not come so rapidly as for the relatively few, more wealthy patients. And of course, Hamilton’s times and therefore also the story of the Hamilton marriage, is drenched in this enormous difference between poor and rich. For Lady Hamilton it will have made a huge difference that the treatment was adapted to the social class the patient came from. I did not know anything about this when I wrote A Victorian Marriage, yet it does not change the fact that after her first long-lasting illness Hamilton will have dreaded the idea that his wife would not be with him any more as I argued on p. 292.

Mauger writes in her The Cost of Insanity, “In 1850, Bloomfield’s managing committee was pleased to report that ‘in the course of the past year the manifest benefit arising from out-door employment, and the steady improvement in the order and discipline of the house which has kept pace with the introduction of means to amuse and employ, have been very gratifying’. ‘Employments of an industrial character, together with suitable recreations, and an enlarged supply of newspapers, periodicals, and useful and entertaining books’ were not only credited with rendering Bloomfield’s patients more comfortable and having ‘fostered habits of self-control and propriety of demeanour’ but also with contributing to the ‘improvement of their bodily health’.”

Having lived in an asylum did not mean however that Lady Hamilton must have suffered from for instance an incurable “nervous illness” or dementia; it is known from Hankins’ 1980 biography that “she was rapidly losing her eyesight,” and from The Cost of Insanity, that “between 1826 and 1867 half of patients admitted to Bloomfield [...] were discharged cured and a further fifth improved or relieved.” This indicates that also a general frailty may have been a reason for Lady Hamilton, who always had a weak health, to admit herself to the asylum.*

From Hankins’s biography it is also known that she could really worry over money, which makes it interesting for her story that in The Cost of Insanity also the fees of Bloomfield Retreat are discussed. “At Bloomfield almost half of recorded fees were over £100. While Bloomfield’s fees were mostly on a par with the private asylums, some patients were kept at lower rates. [...] Bloomfield provided relief for the ‘respectable poor’ as well as the wealthy.” This will have allowed Lady Hamilton to stay there, her pension having been £100 a year, and perhaps having been able to add something from her inheritance.

To complete the story of her last years, it would be interesting to know whether anything has been kept in the records of her time at Bloomfield Retreat; why she came to live there, and what she died from.

* Later note: Together with Dr. William Stokes, Dr. George Wyse was the physician who attended to Hamilton in his last months, indeed up to his very last day. In A Victorian Marriage, I had written that I had not been able to find Wyse’s birth and death years, and in November 2019 Finbarr Connolly also notified me that he had found George Wyse’s day of death. He died on 13 November 1892, in the Richmond Dublin Lunatic Asylum; the male department was at Grangegorman Road Upper. The record shows that Dr. Wyse had lived at 5 Cavendish Row, which Eli and I passed several times in the summer of 2019. Strange, to even recognize the house now.
The fact that Wyse had been very respectable physician but ended his life in an asylum again shows that Lady Hamilton having spent her last days in an asylum does not have to have had anything to do with her two so-called nervous illnesses, of which I showed that they may have been triggered by her difficult position as a married woman in Victorian times having had a distracted husband; the first time from pure happiness, the second time from the devastating news he had received from Catherine.

Addition November 2019: The Quaker Historical Library answered to my question whether there still is information about Lady Hamilton’s stay at Bloomfield retreat, “We have a reference to Lady H’s death in the hospital Minutes. There will certainly be other material. You will be welcome to visit our library and search the records any Thursday morning if that is convenient.” It was also possible to ask them to make a search and provide scans (for a fee), and because I cannot go to Ireland again in the near future, I have asked for such scans. Knowing so exactly how Hamilton died, I am, of course, very curious to know whether also Lady Hamilton still was a bit happy in her last days.



Utrecht, 16 October 2019 — A game and locations in Hamilton’s life, quaternions and spacecraft

Today 176 years ago Hamilton found his quaternions. To celebrate it, a beautiful artwork is made by Emma Ray; a video is made of its creation and shown on one of the pages* of the Royal Irish Academy, which was presided by Hamilton from 1837 until 1846, and is deeply intertwined with Hamilton’s Eureka moment.

* NB. The RIA page suggests that quaternions were used in the Apollo program. However useful the quaternions became, this is not correct, as can for instance be seen here and here. Quaternions were used for the first time in the Space Shuttle program. See also below O’Farrell’s tweet.

Note added the 17th: the DIAS tweeted this atmospheric photo,


Eureka moment artwork by Emma Ray

commenting, “What a day yesterday! Amazing autumnal sunshine for not only the Hamilton walk but the official unveiling of the new artwork commemorating William Rowan Hamilton’s “eureka” moment at what is now Broombridge luas stop.” The artwork even seems to be illuminated at night!

In October 1843 Hamilton was walking to town to preside a meeting of the RIA, when his wife came from somewhere (he must have been deep in thought) and walked with him. She talked with him now and then, and that was when he had his flash of insight. For me reading these sentences in the summer of 2014 gave another flash of thought. I had wondered why such a celebrated man would just marry a ‘local lass from across the fields’; that sounded really very illogical. Reading these peaceful sentences I then suddenly realized: he loved her! If the marriage would have been so unhappy that he had thought, “Woman, go away and let me think!” he hardly would have had a Eureka moment, and mention her so explicitly in connection to his discovery. Of course, that alone was not enough to be certain, but then the long search which followed that thought only made their happy marriage more and more visible, even leading to the question why Hamilton’s biographer Graves loathed her so much. The search for his motives led to the 2017 ‘gossip’ article I wrote with Steven Wepster.

Note added later: Colm Mulcahy sent me a superb tweet written by Anthony O’Farrell on Hamilton day,


I nailed it - O'Farrell

But not only the pun, also the inscription itself is great. Hamilton wrote that having arrived at Broom Bridge he could not “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.” This makes O’Farrell’s inscription, which also will have been ‘mouldered away’ now, the most realistic representation which can be made of Hamilton’s inscription; the only difference being that it was photographed. Which Lady Hamilton doubtlessly also would have done had she had a smartphone, she was very proud of her husband. [Van Weerden 2017, 156]


This year I was very fortunate to be able to contribute something to the celebrations of Hamilton Day. Colm Mulcahy, whom Eli and I met at the 2015 Hamilton Walk, had made a game, to which I contributed a part of the locations. He now asked me to write something about the role these locations played in Hamilton’s life, which I of course happily did, Twenty places in Hamiltons Ireland.

Something else was co-authoring an article for RTE’s Brainstorm, How a 19th century Irish mathematician helped NASA into space. In this article we showed how ubiquitous the use of Hamilton’s quaternions now are in space science. It was a long and very interesting search, emailing with space engineers and searching through the Apollo computer’s code on GitHub. A very informative website, containing many stories and telling photos of what it all looked like in the 1960s, is We hack the Moon. I do not know who made the website, but seeing for instance what computers then looked like, very much enlightened the problems which had to be overcome to make the Apollo program successful.

For me, one of the most interesting ‘discoveries’ was that I had long thought that the fact that the Apollos 10 and 11 almost suffered from gimbal lock was a proof that quaternions were not used in the Apollo program, because quaternions do not suffer from (mathematical) gimbal lock. But then Noel Hughes explained to me that it was a mechanical problem, not a mathematical one. The so-called “stable platform” used for the Apollo’s attitude determination and control had three gimbals, and already using four would have helped. Still, there were good reasons to use only three, and the warnings thought up and programmed by Margaret Hamilton saved the missions. But it had nothing to do with quaternions.



Utrecht, 16 August 2019 — Trinity Library; letters and photos

In the second half of our stay in Dublin we visited Trinity College Library three times. The first day we spent looking through the catalogue, to select the materials we would like to see. The other two days we tried to photograph as much as we could of the materials the staff very kindly brought out for us. What we were searching for was, among other things, whether there was any mention of alcohol abuse by Hamilton from for instance the Board, as you would expect if a professor would really be regarded as alcoholic and perhaps even had crossed borders. We did not find anything in the Minute Books of 1846, 1847 and 1848, although such remarks could have been made in theory. There was an unusual mention of money which Hamilton asked for in connection with the observatory, for instance, he asked for £20 for books.* We also found remarks about Hamilton’s colleague James MacCullagh; as regards his suicide in 1847 there was mention of his burial and the care for his family. But we found nothing about any troubles or complaints concerning Hamilton and alcohol, neither in 1846 around the event at the Geological Society, nor in 1848, when he ended his two years of abstinence.

The most marvellous find I think was a second photo of Lady Hamilton. Although for now it is just a photo taken with Eli’s smartphone, I could not resist making a ‘couple photo’ again which can be seen on the Photo page. To me, it shows what Hamilton’s letters seemed to show, a strong-willed woman, perhaps not always energetic due to her frequent illnesses,** but definitely self-assured; a woman who said openly that she would not become her husband’s slave, and who could indeed enable her husband to work as he needed to.

* In earlier years having applied for books was also mentioned in Graves’ biography [Graves, 1885, 412]. In a time when earning £150 pounds a year was enough to call a man a gentleman [Van Weerden 2017, 167, fn 29], £20 was a large sum of money.

** Despite her frequent illnesses, she does not seem to have been weak inbetween them. She regularly rode her horse, enjoyed visiting and being visited by family members of both sides which then meant a considerable organization of the household, and she prepared for instance luncheons for the public on open days at the observatory.

Something else is that her full name apparently was Helena Maria Hamilton; that her first given name was Helena instead of Helen can also be seen in this Civil List Pensions, and in this picture of Lady Hamilton’s death record in the Dublin Civil records. Indeed also August De Morgan, Hamilton’s correspondent for very many years, had written Helena on p. 130 of his obituary of Hamilton. I therefore changed her name on this website to Helena when her full name is used.

Note added later: In the Wills and Administrations (which Finbarr Connolly pointed me to, see the Addition to Utrecht 19 October 2019), her name is again written as Helen. Still, if both the Civil records, the List of Pensions, the letter which was clearly written by a close acquaintance if not her daughter, and the obituary of De Morgan who was, even though they never meet each other face-to-face, as close as in such a way a family friend can be, all write Helena, then it can safely be assumed that her first given name was indeed Helena. In daily life she was called Helen, and that is how Hamilton and her mother, Mrs Bayly, addressed her in their letters.

In this list it can also be seen how much the pension was; in 1842 it had been £200 per annum [Graves 1885, 450], and although this damaged page seems to read £290, it can be calculated that it was indeed £200.


Combined pages of the Civil Pension List


In time I will transcribe Lady Hamilton’s letters; I photographed all the letters we saw in TCL and now asked for scans. I did not read the letters yet because she wrote them in two and sometimes three orientations on the same page in order to save paper, which will make transcribing them quite a challenge. Yet some sentences I did read already, to see how difficult it would be, and that unexpectedly led to a solution to the question how letters were sent in those days. During their betrothal she wrote to Hamilton that he apparently intended to waste his money on letters. I did not understand what she meant until, coincidentally, two days ago an article was published about the Penny Post; in those years, the betrothal having been in 1833, people did not pay for sending letters, but for receiving them. That made sense; in her eyes Hamilton thus would ‘waste his money’ on letters written by her. From Graves’ biography it can indeed be concluded that she did not like writing letters very much, although she did like reading them [Van Weerden 2017, 294].



Dublin, 3/4 August 2019 — The IHoM5 in Maynooth

Eli and I went to Dublin to attend the joint Irish History of Mathematics (IHoM) and British Society for the History of Mathematics (BSHM) Conference at Maynooth University, where I gave a presentation about the emotional comments Graves made in his biography about Hamilton’s habit of drinking wine, and how later these comments were seen as coming from a trustworthy primary source. I showed what happened at the event in February 1846 with which the Dublin gossip started, and which lead to Hamilton’s alcoholic image. That Hamilton reported to Graves that he had not drunk too much wine, which was directly and indirectly confirmed by other people, and that the question remains why Graves did not defend Hamilton in his biography.

The days of the conference were two very interesting days, in an impressive environment. To walk in the inner square on the South campus, and be surrounded by such stately buildings, was a rare experience. One of the participants of the IHoM5 tweeted a good picture, St. Joseph’s Square.

Hamilton was born at 00:00h, 3/4 Augustus 1805 in Dominick Street. In his younger years, he celebrated his birthday on the 3rd of August, but when his son Archibald was born, on the 4th of August 1835, Hamilton decided to also celebrate his birthday on the 4th. It is very strange to be in Dublin now, at the time of his birth, just two blocks away from Dominick street. The day before yesterday we walked to Dominick Street to look at the house, to see if there is a plaque at the house already, but sadly there is not. Having read that in 1907 there was a tablet on the wall, see Utrecht 18 September 2016, it can be wondered why it was taken off. There may have been practical reasons, but it may also have had to with the then already evolving gossip, as described in the ‘gossip article’. The gossip seems to have started around the beginning of the twentieth century, when Macfarlane wrote the lecture in which he portrayed Hamilton as an unhappily married man who therefore drank much [Van Weerden 2017, 450, ff.]. It would be interesting to try to find why the tablet was removed in the first place, and whether Macfarlane’s lecture had anything to do with it.



Utrecht, 15 June 2019 — Reverend Benjamin Williams Mathias

There does not seem to exist a baptism record of Hamilton, but Graves gives information about the baptism [Graves 1882, 29]. “It will be remembered that the young Hamilton was born on August 3-4, 1805. At the time of his birth in Dominick-street, his father was in the county of Down, arranging business matters consequent on the death of Mr. Gawen Hamilton [(1729-1805)] at Killileagh Castle, but he came up to Dublin to be present at the christening of his child. This took place on the 24th of the same month, the sacred rite being administered by the Rev. B. W. Matthias, the pastor and friend of the family, and then Chaplain of the Bethesda Church, in the parish of St. Mary.”

Searching for information about this “Matthias”, he appeared to be Benjamin Williams Mathias (1772-1841), chaplain of the chapel in Dorset Street, Dublin, from 1805 until 1835, when he became too ill. Indeed, the internet is full of references to Mathias, and there even is a photo coming from his book Twenty-one Sermons (not available online), in the National Library of Ireland Catalogue - The Revd. B.W. Mathias, A.M.. In 1842 a book was published about him, apparently composed using interviews with members of his family, Brief memorials of the Rev B. W. Mathias. Its Preface was written in 1842 by “J.H.S.” of Trinity College; that will have been Joseph Henderson Singer (1786–1866) who was, around the time of writing, Professor of Modern History and one of the University preachers at TCD. Like Mathias, Singer was Evangelical, and together Mathias and Singer founded the Hibernian Bible Society.

Mathias was famous for his sermons; it has been mentioned about him that he was “Dublin’s most popular Anglican evangelical preacher,” and that “his congregation was one of the most influential ever assembled in Ireland.” “When Mr. Mathias and his colleague, the Rev. W. Thorpe, first began to preach at Bethesda [A.D. 1805], the congregation was very small, scarcely more than fifty persons attending [...]. The numbers that now began to frequent Bethesda were very great. Some came at first from motives of mere curiosity; others, because they liked the music, or heard that the service was performed with solemnity; but these were, in most instances, kept there as stated hearers, by love for that Gospel which they had formerly slighted, but which had now reached their hearts.” [Brief Memorials, 149-150]. The Oxford Dictionary of National Biography writes (not open access), “He was soon one of the most popular evangelical ministers in the city, his preaching being considered so powerful that the provost of Trinity College, Dublin, forbade students from attending his services.”

From the Preface of the Brief Memorials it appears that at some time Mathias had been prohibited from preaching. It was written in 1842, just after the publication of the last Tract of the Oxford Movement, which to outsiders as I am explains the terms ‘high’ and ‘low’ used in the Preface. ‘High’ was used for the movement that emphasized the Catholic heritage of the Anglican church, and ‘low’ for the Anglican Evangelicals, who stressed the Protestant heritage. “In doctrine, Mr. Mathias was what is generally understood by a moderate Calvinist; differing in opinion from the eminent reformer from whom that name has been taken on some of those points on which it may be said he will be found to have differed from himself. [...] As a singular but decisive proof that the inhibition was directed not against any supposed irregularity in Mr. Mathias’s ministrations, but against the Calvinism he was supposed to preach,* it may be mentioned that the respected prelate who prevented him preaching in any of the churches in the diocese, had been in the habit, almost up to the time of the inhibition, of attending Mr. Mathias’s preaching in Bethesda. The inhibition was taken off [...] by Archbishop Magee, who licensed Mr. Mathias.” [Preface, xix - xx, xviii].

Mathias had been a friend of Hamilton’s parents and indeed, Graves mentioned about Hamilton’s father that he had been “a man of great energy and strong impulses, of remarkable business powers, of exuberant eloquence, both of the pen and lips, of strict evangelical views of religion, and of zeal in expounding and enforcing them, but withal of tender affections, and a convivial disposition.” [Graves 1882, 9]. Hankins described Hamilton’s temporary leanings to high churchism which lasted from, most likely, 1839, until late 1845 or very early 1846, and in 1858 Hamilton again referred to himself as an Evangelical Anglican [Hankins 1980, part 5 chapter 16.]

In any case during Hamilton’s “High Church Days”, as Hamilton’s son William Edwin called his most extreme years, but also after his 1845/1846 “cooling down,” as Hankins called it, if Mathias leaned to Calvinism, then that must have been difficult for Hamilton. He was very negative about Calvinism, writing that “[Calvinism is] a System of Theology, which, if it had been imposed by external authority upon me, would have gone near to making me an infidel.” But in his biography Graves did not mention Mathias any more and he hardly wrote about Hamilton’s “private friends;” without reading Hamilton’s notes and letters it is therefore not known what exactly Hamilton thought about it.

In his younger years Hamilton’s political ideas were more like those of uncle James than of his father. In 1852 Hamilton wrote to De Morgan, “From childhood I have had political leanings, and always to the illiberal side. My father (Archibald Hamilton, of Dominick-street, Dublin) was a liberal, almost a rebel; he assisted Hamilton Rowan to escape from prison, and deeply involved himself by other efforts in his favour. On the other hand, his brother, my uncle, the Rev. James Hamilton, who lived for forty years the Curate of Trim, and died as such, was a Tory to the back-bone, and doubtless taught me Toryism along with Church of Englandism, Hebrew, and Sanskrit — that last acquisition being pretty well lost by this time, although I still like the look of the letters! My father used to enjoy the provoking me into some political or other argument, in which I always took my uncle’s side.”

About his later years, in 1855 he wrote to Speranza, “[I am] essentially an Irishman by birth, and life, and labour, though educated by a clergyman [uncle James] who held the ascendancy principles (from which, by very slow degrees, I have been through life gradually emancipating myself), and who would have regarded repeal as rebellion. It was English history, not Irish which I was taught; and my heart still throbs with sympathy for that great British Empire to which, from childhood, I have been accustomed to consider myself as belonging as to my country — though Ireland, as Ireland, has always been the object of my love — and, I think you will admit, of my exertions.”

Therefore, having gradually ‘emancipated’ from his uncle’s political opinions, and in 1858 referring to himself again as an Evangelical, it is remarkable that in later life Hamilton returned, even if it was only slightly, to his father’s ideas both politically and theologically.** It can be imagined that that would have made Archibald Hamilton even more proud of his son than he had been already.***

* In The Evangelical Magazine and Missionary Chronicle, volume 19, 1841, Mathias is mentioned in a list of “Dissenters.” Not about Mathias in person, but showing what it was about: before giving the list it was written, “Clerical Irregularities. We believe that some clergyman of our Anglican Church preaches every day in London, in the month of May, for the London Missionary Society — a society of Dissenters, formed for the express purpose of sending out Dissenting missionaries.[...] It is, indeed, a remarkable fact, that the clergymen who give their churches for this object, and those who preach the sermons, are men, in every instance, who pay little regard to the canons, rubrics, and discipline of the Church, to whose formularies they have solemnly subscribed, or to their diocesans, to whom they have sworn to pay canonical obedience.” The list of Dissenters, including “Rev B.W Matthias, A.M., Chaplain of Bethesda, Dublin,” can be found on page 493.

** Admittedly, this is as how it is seen from far outside Ireland, and I do understand that there are very many nuances which are hard to grasp for interested non-Irish. The human side of Hamilton’s story is universal (unhappy alcoholics do not produce so much innovative and beautiful mathematics wherever they come from), but the political and theological side is not.

*** Archibald Hamilton had indeed been very proud. Hamilton continued the 1852 letter to De Morgan: “The seal, which I still use, and which contains a sort of abridgment of my father’s arms, was given me by a maiden aunt, Miss Hutton, on the occasion of my triumphantly winning, as my father more triumphantly confessed to some friends (or flatterers) whom he had collected, in a contest of eloquence with himself for my first watch, which, when I was about twelve years old, he affected to deny that he had promised me.”



Utrecht, 19 May 2019 — Uncle James, his family and the Diocesan School

Modified 2 November 2019


Uncle James’ family

In my Hamilton essay I had assumed that in 1808, when the young Hamilton came to live with him in Trim, uncle James Hamilton (1776-1847) already had a family of his own. I had not given that much thought, but rereading the census of 1821, and now again knowing more than I did then, I suddenly realized that if aunt Elizabeth was 29 in 1821 she would not have been married already in 1808. I then found that they married on 10 Feb 1814, when Hamilton was eight years old.


Marriage record James Hamilton and Elizabeth Boyle


Marriage record of James Hamilton and Elizabeth Boyle. The record is the third one in 1814, the fourth from the top. It is recorded that Elizabeth was a spinster, that the marriage was consistorial, and that they were married by R. Vicars. “Do” in the one but last column stands for Ditto, or idem.



Irish census 1821 Trim Manorland Hamilton


Uncle James’ family in the 1821 Irish census record. The census, given on the website of The National Archives of Ireland, was held in the night of Monday 28 May 1821. Every person in the house was registered, independently of whether they lived there, or were on a visit. While writing my book I did not understand what “Clerk Rector of Armorish” meant, but uncle James also was rector of Almoritia [Graves 1882, 24-25]. Graves did not know when uncle James became rector exactly, but he may have been sworn in after the rebuilding of the St. Nicholas Church in ca 1816. Almoritia was also called Almorita, Moranstown or Ballymoran, now Ballymorin, County Westmeath.


In his family tree, Graves first gave the sons, then the daughters, making it impossible to place the children in the order of their ages. Yet in accordance with the order of the daughters in the family tree, from the census record it can be seen that Elizabeth was the eldest child; having been six in 1821 there is hardly room for an older child. After the census ten more children were born about whom there is hardly any direct information, but Graves mentioned in his family tree that of the thirteen children four died young, two sons and two daughters. The names of the sons are unknown, but the daughters were found, Kate and Charlotte. Kate must have been born after May 1821 because she is not in the census, yet on 21 April 1822 Hamilton wrote that on Thursday 18 April they had attended Kate’s funeral, and that “she was laid by the side of her little brother and mine.” Kate thus must have been born shortly after the census, and one of the unknown sons apparently died in any case before April 1822. Of Charlotte it is known that she died in June 1845 at her parent’s home, St. Mary’s Abbey. If she indeed died young she may have been born when aunt Elizabeth was fifty already.

Because in a newspaper article it was mentioned that Francis was the second son, which is in accordance with Graves’ family tree, and the order of the eldest daughters in the census is the same, it will be assumed that also for the other children the order in the family tree is correct. The latest known date of the birth of a child in the Hamilton household was 1835, when on 20 January a daughter was born. The birth years of the four eldest daughters are known up to a year, as is the birth year of Francis Cecil, and combining these data with other newspaper articles, this is what I reconstructed, Family of Uncle James.

The last years of uncle James and aunt Elizabeth must have been very difficult, and the fate of their family was what happened to many families in those days. Next to the four children who had died young, between 1844 and 1846 also four of the other nine children died. In 1844 both Mary (ca 24) and Gracey (ca 26), in 1845 Charlotte (most likely still very young), and in 1846 Francis (20). Uncle James died in 1847, and aunt Elizabeth in 1848.


Uncle James

Uncle James was, in any case since 1802, curate in Trim, which he would remain until his death in 1847. And from 1813 he was rector of Almoritia, “a small rural parish in the neighbourhood,” [Graves 1882, 24], see also Hamilton’s poem on [Graves 1882, 132]. But there are only a few descriptions of uncle James as a person.

One of the descriptions was given by his son James Alexander. Preparing for the biography, Graves had asked James Alexander for letters written by his father, and he had answered, “my dear father ... who was indeed a man of great ability and learning, and of most charming versatility, as well as power and originality of mind, was not systematic, or careful of his papers: and I have often grieved to think that there remain the merest scraps and remnants of them, sufficient to indicate in the vaguest way the learning, research, refined and critical taste, poetry, philosophy, wit, pathos and sentiment, of which he was full, and which I seem to remember more distinctly, and value more fully in my old age, than in former years.”

Another short description was given by Harriet Butler. From 1770 until 1818 William Elliott (..-1818) had been vicar of Trim; he features in one of the remarkable stories of Hamilton’s childhood [Graves 1882, 33]. He was succeeded by Richard Butler (.. -1841), but due to health problems already a year later Richard Butler asked his son, who was also called Richard (1794-1862) to succeed him. This Richard Butler married Harriet Edgeworth (1801-1889), one of Maria Edgeworths half-sisters, and she wrote A Memoir of the Very Rev. Richard Butler : Dean of Clonmacnois, and Vicar of Trim. By his widow (containing a picture of Butler). In this memoir, she does give a short description of uncle James.

She writes about Butler’s arrival in Trim, “Mr. Elliot’s curate, the Rev. James Hamilton, was many years older than his new vicar, which might well have caused a jealousy in his feelings that would have made their mutual relations unpleasant; but, on the contrary, he from the very first made him his friend, and for seven years [from his arrival in 1819 until their marriage in 1826], when not otherwise engaged, Mr. Butler spent his evenings with Mr. and Mrs. Hamilton and their children at St. Mary’s — a curious and interesting old house, part of the monastery of St. Mary’s.* Mr Hamilton’s great learning, taste for literature, and originality of mind, were not only agreeable, but of great use in keeping up his classical studies and scholastic thoughts.” [A Memoir, 16-17].

* The house was also called Talbot’s Castle, see pp. iv and 19 of her husband’s book Some Notices of the Castle and of The Abbies and other Religious Houses at Trim.


The Diocesan School

Next to having been curate of Trim, uncle James also was schoolmaster of the Diocesan School. In the first version of my sketch about Catherine Disney I had suggested that one of the reasons that Hamilton’s parents decided to send him to Trim was that uncle James was teaching in “one of the best schools in Ireland.” That reference came from Lluís Barbé’s 2010 biography of Francis Ysidro Edgeworth, in which he also wrote that the school in Trim had been run by Richard Butler “with the help of James Hamilton.” But in her Memoir Harriet Butler mentioned that her husband started a parish school at his own expense, “a free school — he paid the [excellent] master [Mr. George Mooney] himself; and it was attended by all the Protestant, and some Roman Catholic boys and girls.” Mooney had been master of the Charter school in Trim, and “on the dissolution of the Charter School, [Butler] obtained leave from the Incorporated Society to have the day-school continued there. There it continued as long as he lived, and he seldom passed a week when at home without visiting it, cheering the teacher and encouraging the children.”**

Harriet Butler’s remark could mean that that very good school was not the diocesan school which Hamilton attended, but Richard Butler’s day-school, although Barbé’s explicit mention of uncle James does make that less plausible. But even if it was one of the best schools, it is still possible that it only became such a good school after Butler arrived. Robert Butler having started in Trim in 1819, he was not there yet when in 1808 Hamilton came to live in Trim, and my suggestion about Hamilton’s parent’s motives, that the school was one of the best schools in Ireland, is therefore possible, but not certain. That does not change the fact however that Hamilton’s parents very rightfully trusted that their son would be thoroughly educated by uncle James.

It is not known when the Diocesan school in Trim was founded. On p. 128 of the thesis The Archaeology and History of Medieval Trim, County Meath, it is stated that there had been a diocesan grammar school in Trim from at least 1567, “but one cannot be sure of its location until the eighteenth century.”*** Thereafter the Diocesan school was housed in St. Mary’s Abbey, or Talbot’s Castle, and also uncle James lived there with his family and some of the boys attending school, as was seen in the 1821 census**** and mentioned by Richard Butler on p. 9 of his 1835 Some Notices of the Castle and of the Ecclesiastical Buildings of Trim, or the 1861 fourth edition. About Talbot’s Castle having been built in the first half of the fifteenth century he writes, “During his different lieutenancies [1414-1421, 1425, 1446], [John] Talbot [(ca 1387-1453)] resided frequently in Trim; and then, probably, built the castle now [1835] occupied by the Rev. Mr. [James] Hamilton, and which is called Talbot’s Castle in the town records. [...] This house was formerly the Diocesan School of Meath, and built by the great terror of the French [Talbot], it was the place of the early education of the Duke of Wellington [(1769-1852)].”

In conclusion, combining all this data, it can be concluded with confidence that Barbé was right when he stated that the school where uncle James became School Master was the same school as mentioned in connection to the Duke of Wellington. If he then was also correct about the school having been one of the best schools in Ireland, the choice of Hamilton’s parents to send their young prodigy to Trim is even more intelligble. They were very lucky to have that opportunity, and Hamilton’s life would perhaps have looked quite different if he had not had such an opportunity so very early in his life. Being loved by his family, and educated on such a high level within the extended family is a privilege not many children experience. I now am sorry that I deleted Barbé’s remark from Catherine Disney’s biographical sketch, although I still do not know where the claim of having been one of the best schools in Ireland came from.

** Trim was apparently large enough to have more than one school, or even, in any case in 1835, eight schools. See for Butler’s “National Model School” also Eugene Alfred Conwell’s 1878 A Ramble Round Trim.

*** Chapter 9 of this thesis, starting on p. 125, discusses the history of Talbot’s Castle. It contains photos of details of Talbot’s Castle, “locally more commonly known as St. Mary’s Abbey,” where Hamilton grew up.

**** Uncle James’s address was usually given as St. Mary’s Abbey. For instance, in the 1835 Proceedings of the Fifth Meeting of the British Association it is given in the list of members and subscribers, in the left column at about the middle of the page. The star means that he was a member of the General Committee. In the 1821 census the address was given as 215 Manorland, which may have been the official address.


The Diocesan School house as the Hamilton’s family home


Irish census 1821 Trim Manorland Hamilton original form



Richard Butler’s above mentioned text about uncle James and Talbot’s Castle is not unambiguous; it leaves the possibility that James Hamilton moved in after the school had been discontinued. Yet Harriet Butler mentioned that before their marriage in 1826 her later husband very regularly visited the Hamiltons in St. Mary’s, therefore uncle James and aunt Sydney will already have lived there when Hamilton came to Trim in 1808.

The original form of the census of 1821 gives more information than the more readable pdf given above. At the top it reads, “No.1. Townland of Manorland in the Parish of Trim. Part of the town of Trim on the North side of the Boyne. Barony of Upper Navan and County of Meath. Behind Grace Hamilton’s name it is mentioned that she was a Niece, a Spinster, and “here on a visit.” Behind James Hamilton’s name it has been written, “Clerk Rector of Armorish & Piercetown Parish: Co. of Westmeath a Curate in the Parish of Trim and Master of the Diosean School of Meath.” In Lewis’ 1840 A topographical dictionary of Ireland Almoritia is described; Piercetown was united episcopally with Almoritia in 1791. The second remark on the right page of the census form is more general, “Within a few perches of the Diosean School stands a ruin called the Yellow Steeple. Supposed to be near 100 feet high. Great part of which is said to have been blown down by a storm not many years back.” The fourth remark reads, “The remainder of the Tower of Trim is on the North ?? adjoining the Town of Trim and part of the Manorland.” “Do” in the fifth column stands for Ditto, or idem. The three boys attending school and living with the Hamiltons thus were John Butler, William Hamilton and Abraham Bradley King. The three house servants, apparently also living there, were Elizabeth Hughes, Mary Morgan, and Mary Burke.

At the time of the census Richard Butler, who had been vicar of Trim since 1819, had not married yet, and a remark next to Manorland 217 reveals that the Hamiltons and Butler were neighbours although that could not be seen directly in the census. “This is the glebe house in which the Rev Richard Butler Vicar of the Parish of Trim reside adjoining the Tower of Trim & part of Manorland. Mr Butler was sayd to be absent in Scotland at the time of Taking the Population of this house but is since returned.” The 6th column, No of acres, is empty, meaning that the people on this form did not own land.



Talbot’s Castle


In this Google street view Talbot’s Castle is seen from the grounds of Trim Castle. It does not look like a castle; the ruinous structure which can be seen on the right is the Yellow Steeple. Yet Talbot’s Castle is a large building, probably large enough to house both a small school and a family.



Griffith’s Valuation, Trim map, between 1848 and 1864


In the 1821 census the family’s address is given as 215 Manorland, which would suggest that it was on the south side of the river Boyne. This historical map can be seen on Ask about Ireland, choose Griffths Places, Trim, region Meath, barony Navan Upper, then choose any map. In this map it can be seen that Manorland is indeed mainly located at the south of the river Boyne, but a small part extends to the north, and comprises Talbot’s castle, Trim Castle, and Trim’s New Gaol which was opened in 1834. The old gaol can be seen to also have been close-by; the inhabitant of Manorland 211 was a Keeper of the Gaol.


The end of the Diocesan School

Although it is not known when the Diocesan School was founded, it is known when it was discontinued. On p. 6 of the Fifth Report of the Commissioners of Irish Education Inquiry it can be read that in 1823 “the Commissioners made to His Excellency the Lord Lieutenant a special report on the Diocesan Schools.” Next to many recommendations, they also “recommended that the School of the Diocese of Ardagh should be united with that of Meath, so as to form a District School to be placed in the populous town of Mullingar, in the Diocese of Meath, and that the School-house of the Diocese of Ardagh at Longford, and the School-house of the Diocese of Meath at Trim, should be sold towards founding the District School at Mullingar.”

Combining advertisements on Genes Reunited : SBNA, keywords: diocesan school house trim, years: 1828-1829, it can be seen that the house was offered for sale in August 1828, “Houses to be sold. Situate in the towns of Longford and Trim, to be sold, by the Commissioners of Education, the Diocesan School House in Longford, and the Diocesan School House in Trim. Proposals to be directed to William Charles Quin, Esq. Secretary to the Commissioners.” In June 1829 it still was for sale, “To be sold by the Commissioners of Education, and in immediate possession given, the Diocesan School, house and Garden, situate in the town of Trim. The Premises are held in fee simple. Proposals to be directed to W. C. Quin, Esq, No. 11, Stephen’s-green, North.” In 1830 it was sold; an advertisement of June 1830 reads, “With view of creating a fund to build a school-house at Mullingar, for the districts composed of the dioceses of Meath and Ardagh, we caused to be sold the old school-houses of those dioceses, for the sum of £380.”

In House of Lords : the Sessional Papers 1801-1833, Vol. 271, 1830, on p. 447, which is p. 5 of the Annual Report from the Commissioners of Education in Ireland : For the Year ending 25th March 1830, the Commissioners write, “[We have to state] that with the view of creating a fund to build a School House at Mullingar, for the District composed of the Dioceses of Meath and Ardagh, we caused to be sold the old School Houses of those Dioceses, for the sum of £380, the balance of which, after deducting £1 15s., the expense of an advertisement for sale of the Diocesan School House of Meath, we have invested in Government Stock to the credit of the said District School.”

It is not known to whom Talbot’s Castle was sold, and why the Hamiltons could stay there. Uncle James died in 1847, and aunt Elizabeth in 1848, but in any case in 1858 family members still lived there; that year Hamilton wrote to Augustus De Morgan, “I received your note of August 21, but started almost immediately afterwards for St. Mary’s Abbey, Trim, where my dear daughter Helen was on a visit to some cousins of mine, and was then dangerously ill” [Graves 1889, 554]. The “cousins” still living then were Sydney, Catharine Frances, Margaret Octavia and Anna Sophia. But if Catharine indeed had married the reverend Samuel Slater as suggested in Family of Uncle James, she then lived in Calcutta. The cousins in Trim then were Sydney, Margaret Octavia and Anna Sophia.


Temperance in Trim

Mrs. Harriet Butler gives a vivid description of temperance in Trim which is for Hamilton’s story too interesting to leave out, partly because he was obviously not the only one who did not ‘join the temperate society,’ and partly because in the last line it can be seen how little people then knew about the effects of alcohol in the longer term.

“The temperance movement had been for some time going on throughout Ireland, and on St. Patrick’s day 1841, a great procession went out to welcome Father Mathew: all the tallest and finest looking young men dressed in their best, and wearing blue scarfs, walked two and two, preceded by a band, which Father Halligan, the curate, had been at great pains to form and instruct and which he accompanied on horseback. It was a pretty sight, and multitudes came next day to receive the pledge. Father Mathew kindly called on Mr. Butler after the labours of the pledge-giving were over. Not tall, and rather stout, with fine regular features, he had a mild, benevolent expression of countenance, with most pleasing, perfectly unaffected manners. He said it was not he himself who had originated the plan of giving and taking a written pledge with a medal. A Quaker, at a temperance meeting, suggested it, and Father Mathew had adopted and carried it into effect.

“Mr. O’Connell, the priest, was too sensible a man to suppose that an enthusiasm of this kind could last; he said it was contrary to human nature, and did not himself join the temperance society, but he gave every encouragement to his curate, and all who chose to join it. The perfect sobriety of the next three years almost conquered his disbelief in the power of the pledge: indeed, though it was a fact, it seemed an impossibility. By degrees, however, the fervour of faith faded away. Father Mathew returned no more; temperance cordials were resorted to, and the respect for their vow became fainter, many broke it, and there were no new takers of the pledge; but many kept and keep it, and to be drunk is still disreputable. And one fact was proved, that sudden and complete abstinence from fermented liquors, in those accustomed to take it in large quantities, was not, as had been formerly asserted, fatal to the constitution, but immediately and permanently beneficial to the health.”



Utrecht, 4 May 2019 — Illnesses and astronomy

When I started, in 2014, on my Hamilton essay, I had not doubted the general view that Hamilton did not like practical astronomy because he preferred mathematics, see meteors. But when I was writing the sketch about Catherine Disney I had to reread Hamilton’s early years, and I then started to realize that the referrals to his illnesses were more frequent than I had noticed earlier. For instance, Hamilton had whooping-cough in 1822, and in 1823 his entrance into college was even postponed by half a year because of his bad health; he had “coughed much, and had to struggle with great difficulty of breathing.”

Early in 1826 Hamilton suffered from a “long and painful illness”, and Graves wrote about 1827 that “the commencement of Hamilton’s practice as an Observer rather seriously affected his health. He suffered from constant cold in head and chest, and was much of his time confined to the house.” His bronchitis stayed with Hamilton his whole life; about Hamilton’s last weeks Graves wrote that he “corrected for the press his Papers for the Proceedings of the Academy; but soon bronchitis supervened, and, with other ailments, led on to the inevitable close.”

My unpublished (and later again revised) article about Hamilton’s enthusiasm for special astronomical events as eclipses, comets and meteors, something which has often been overshadowed by the negative look on his astronomy, and the apparent consequences of his illnesses for his practical astronomy, can be found here, Illnesses and Astronomy.

Note added 4 Aug 2019: During the IHoM4 of 2017, Miguel DeArce gave a presentation in which he showed that taking Hamilton’s education into account, and his good knowledge of positional astronomy, it had indeed not come “out of the blue” that Hamilton became Andrews Professor of Astronomy when he was 22. See: The Pre-History of Genius: William Rowan Hamilton’s school days in Trim, Co. Meath (1808-1823).



Utrecht, 18 January 2019 — An article about the largely ignored influence of Helen Bayly and Catherine Disney on Hamilton’s life

An article about the influence of Helen Bayly and Catherine Disney has been published in the Bulletin of the Irish Mathematical Society. In the article I argue that one of the reasons that the caricatural view on Hamilton could arise from Graves’ biography was that the influence of these two women on his life was not accounted for. It made them look static, as if in their private life nothing ever changed, as if they just were a semi-invalid (Bayly), a beautiful romantic ideal (Disney), and a simple zealous great man (Hamilton). Yet much happened because of their relationships with other people, which influenced their lives and changed them over time, something which of course happens with almost everyone.

I do realize that even in this article nothing further is said about Catherine, again leaving her almost unknown. That is due to her largely passive role in Hamilton’s later life; after her marriage they only met a few times. From Graves’ biography some important things about Lady Hamilton could be deduced because every now and then she was present in his descriptions, either because Graves wanted to criticise her, or she was mentioned in Hamilton’s letters and he could not leave her out. But that did not hold for Catherine. Graves felt that he had to leave her out as much as he could, because they were married people. It led to Catherine being reduced to a lost love, a romantic ideal, and Hamilton to a hopeless romantic.

In the article I made some errors. On p. 95 I wrote that Hamilton was Astronomer Royal which is the title of the English astronomer; it should have been Royal Astronomer of Ireland. And on p. 93 I wrote that Graves took care not to reveal Catherine’s identity, but I forgot to add ‘in the main text’, because he did give her name in the index. Referring to the 1850 story of the “lady’s dog“ in Summerhill, and Catherine‘s death “early in November” 1853, Graves wrote in the index: “Disney, Catherine, 648. Her death, 691.” The only time he really concealed her identity was when he gave the ‘Extracts’ of the 1848 correspondence between Hamilton and Catherine. That that were extracts from letters to Catherine only became widely known when Hankins published his biography in 1980.



Utrecht, 11 November 2018 — Photos of Hamilton and his notebook, also showing Graves’ blue pencil

On the 175th birthday of the quaternions, the 16th of October 2018, TCD Research Collections tweeted two photos I had not seen before. The first one shows Hamilton, apparently in the early 1860s because his hair seems a bit more grey than on the 1859 photo which was shown by Graves as a frontispiece of the second volume of his biography, but not so grey as in the 1864 photo. The photo is clearly showing black spots and I decided to try to remove the ones on his face; what I made of it can be seen here. Because I did not see the real photo I can be wrong, therefore I also show the original and the adapted one together, to make it more easy to compare them.

The second photo shows the page of the notebook in which Hamilton wrote the quaternion equations while he was walking with his wife along the Royal Canal. I had never seen it in other form than black and white, and therefore I did not know that it was written with a pencil instead of with ink as I had assumed. Hamilton did mention that he had pencilled it, but I had not really realized that a pencil was not a pen (in Dutch the words are very different from each other, namely pen and potlood). And I did not know that the remark “xx important” was written in blue! The tweet linked to an online exhibition about Erwin Schrödinger, and also on another page thereof, containing parts from Hamilton’s work on his ‘Theory of Systems of Rays’, there are notes written with the same blue pencil. In his 1980 biography Hankins remarked that when he saw Hamilton’s correspondences in Trinity College Dublin Library he could see that Graves had also read most of these letters by the “ubiquity of his blue pen” [Hankins, 1980, xxi]. The ‘important’ remark on the notebook page will therefore have been written by Graves instead of by Hamilton. That would completely explain why Graves had not mentioned it when he transcribed the pocketbook page [Graves 1885, 437], something I had not noticed when I wrote the essay.


Pocket-book page with the first quaternion equations


The pocket-book page with the very first quaternion notes. With    is Moon-day and ocer is October, the date reads ‘Monday October 16 1843.’ With eqns is ‘equations’,  ∀  is ‘and’, and R. I. A. is the abbreviation for the Royal Irish Academy, according to Graves at the bottom of the page Hamilton wrote, “I showed these equations, and gave an account of their meaning to Dr. MacCullagh and the Rev. W Sadleir to-day, October 16, 1843, at the Royal Irish Academy.” With his blue pencil, at the top Graves wrote “xx important”, he underlined the date, and at the bottom he underlined MacCullagh’s name.
Paraphrasing small parts of letters and notes, what happened is that having had his flash of insight, Hamilton pulled out, on the spot, this pocket-book and made an entry. He then could not resist the impulse to cut with a knife on a stone of Brougham Bridge, as they passed it, the fundamental formula which, as an inscription, has long since mouldered away. Then in a jolted handwriting, the same pencilled page contains the four quadrinomial constituents, which were inserted while he was driving on that memorable Monday from the neighbourhood of the turn-pike to the Academy. Still in the car he checked the law of the moduli using the dots, and he wrote the second page with the plus minus terms when sitting in the president’s chair of the R.I.A. It can be seen that on the second (upper) page, in a less “jolted” handwriting, he rewrote and rearranged the five terms with the (four) plus-minus signs from the first (lower) page, and added the other four terms. [Graves 1885, 437], [Van Weerden, 2017, 8-14].
Reproduced from artsandculture.google.com. The picture of the second notebook page was tweeted by Peter Gallagher of TCD on the 14th of May 2019.

I then realized that I had already seen this blue pencil. When in 2015 we were in Dublin, we tried to find when exactly Hamilton’s father had bought the house in Dominick street, and we therefore visited the Registry of Deeds at The King’s Inns. I clearly remember that in one of those books I also saw that blue pencil because I made a remark about it to Eli, but then I did not have all the facts as ready as I have now, and I was unsure whether the bankruptcy of Archibald Hamilton, which was mentioned in one of the books, really concerned Hamilton’s father because more Hamilton families appeared to have lived in Dominick Street. I do not remember if the blue note and the bankruptcy were connected other than that I saw them both on that afternoon, yet it is in some of these enormous books, and it should not be very hard to find if someone is interested.

It sounds in any case very logical that also Graves consulted those books; he learned to know Hamilton in 1823,* when Hamilton befriended his elder brother John Thomas Graves, and writing the biography he therefore had to do much research about Hamilton’s childhood. It does feel a bit odd though that he would write so clearly on Hamilton’s notebook page, I do not think any one would dare to make such a note on such an historic piece of paper. But for Graves that was of course very different, living in those times, knowing Hamilton very well and not particularly liking the quaternions, or rather Hamilton’s focus on them [Van Weerden, 2017, 486].

* From a remark in the biography it seemed that Graves had learned to know Hamilton much earlier, namely when he wrote about Hamilton that “his father’s death became in the onward course of his life a new point of departure, and from that time we shall see the boy rapidly changing into the man.” But in his 1842 article in the Dublin University Magazine, on the second page, he wrote that he had heard about Hamilton long before he “ever saw” him. He thus will have alluded to the letters in which it could be read that Hamilton rapidly matured.

Searching on the internet for more versions of both tweeted photos, I came across a photo of the outside of the notebook, which was also surprising. Hamilton remarked in one of his manuscript books about it, “the pocket-book remains, given me by Helen in 1840, in which, while I was walking to town on the day [of the discovery of the quaternions], I did actually pencil at the time, and just as I reached [Brougham] Bridge [...], the [fundamental equations]” [Graves 1885, 437]. It is very special to be able to see it; the lock and green leather seem to show that it was not just an ordinary notebook, that it thus was a real gift.


Pocket book by Helen Hamilton 1840 1843


This is the pocket-book Helen had given her husband in 1840. Hamilton wrote the fundamental equations in this pocket-book before they reached “Brougham Bridge.”**
Reproduced from artsandculture.google.com.




** In his 2007 It’s Part of What We Are, Charles Mollan writes, “Ian Elliott has suggested [in personal communication] that Hamilton used the wrong name on purpose. The bridge was originally named after William Broome, Director of the Royal Canal Company, who lived nearby. But Hamilton was an admirer of the great Whig politician Lord Henry Brougham (1778-1868), educationalist and defender of the particle theory of light. Brougham is also remembered for the type of one-horse carriage which was first made for him. Further, Hamilton’s mother, Sarah Hutton, was a member of the coach-building firm located in Summerhill in Dublin, which made the Irish State Coach for Queen Victoria, and also made Brougham coaches. So calling the Bridge Brougham Bridge (pronounced the same as Broome) could well have been a family in-joke. Nice theory.”



Utrecht, 20 September 2018 — Calculating, quaternions, Gibbs and computers

It is well-known that Hamilton was a master in calculating in his head. Even in his last years he learned new ways of calculating: one which he adopted from his astronomy assistant Charles Thompson, and one which was invented by Mr. Boyers, one of his nephew John Rathborne’s employees; Boyers had devised a system of contracted multiplication which Hamilton considered to be “new and ingenious.” That Hamilton indeed loved to calculate can for instance be seen in the very last article he sent to the Philosophical Magazine, which was about Röber’s construction of the heptagon in connection to the Temple of Edfu. It is filled with very precise calculations, to which is added a footnote, that the actual computations all had “been carried to several decimal places beyond what are here set down.” And in a footnote on the last page Hamilton remarks, “Some friends of the writer may be glad to know that these long arithmetical calculations have been to him rather a relaxation than a distraction from his more habitual studies.”

Quaternions involve very extensive calculations, but the ‘experienced calculator’ Hamilton was, he never seems to have regarded that as an obstacle for the use of quaternions; had he done so he would perhaps already have thought of splitting the quaternion product into the scalar and the vector part. It can easily be argued that the fact that Hamilton failed to acknowledge the long calculations as an obstacle was one of the main reasons for the disappearance of the quaternions in physics after the emergence of vector analysis. Whatever the mathematical advantages of quaternions were, vectors are much more intuitive, and for physicists much more easy to work with, as Gibbs clearly indicated in the ‘abstract’ to his pamphlet.* But so assuming that the length of the quaternion calculations was one of the main reasons for the disappearance of the quaternions, it can also be argued that the computers were the main reason for their reappearance in physics; computers simply do not mind to calculate as Hamilton did.

Such a simple view on the disappearance and reappearance of the quaternions in physics would again shed light on Hamilton’s bad luck, and it certainly needs a lot of bad luck to have such a terrible private reputation while leaving such an enormous mathematical legacy. Hamilton liked to drink alcohol in the times of the temperance movements, he found his quaternions before the invention of computers, and he lost his first love due to circumstances they both were unable to influence. Nowadays drinking alcohol is socially accepted, quaternions are used more and more by the year now, and television programs are made about people who share the fate of William and Catherine, without their marriages being doubted. It can be said that Hamilton’s misfortune mostly was that he lived in the wrong times.

* In his 2002 talk A History of Vector Analysis, Michael Crowe mentioned about the ‘abstract’ of Gibbs’ pamphlet that in 1888 Gibbs wrote to Victor Schlegel, ““After learning a little of Grassmann, “I saw that the methods wh. I was using, while nearly those of Hamilton, were almost exactly those of Grassmann.” Gibbs recounts that he then procured copies of Grassmann’s Ausdehnungslehre volumes, struggled with them, but adds: “I am not however conscious that Grassmann’s writings exerted any particular influence on my VA, although I was glad enough in the introductory paragraph to shelter myself behind one or two distinguished names....” In summary, Gibbs adds that that he hopes Schlegel will be interested to know “how commencing with some knowledge of Ham[ilton]’s methods & influenced simply by a desire to obtain the simplest algebra ... I was led essentially to Grassmann’s algebra of vectors, independently of any influence from him....”



Utrecht, 30 June 2018 — Extreme honesty and eccentricity, a happy marriage and drinking prowess, and still evolving gossip

It was stated by his friends that Hamilton was extremely honest. De Morgan wrote: “In the matter of right and wrong, Hamilton was very simple-minded. To say he was truthful would be only a part of the truth; his aptitude to entertain misgivings [...] made him often think it right to express his opinions to avoid the possibility of being misunderstood. But it may be said that it was not he and others who differed, but his opinions and the opinions of others; his tolerance was perfect.”

Another aspect of Hamilton was that he does not seem to have cared much for his reputation amongst people outside science or his private life. De Vere wrote about him: “It was impossible for the most careless observer not to be struck by him at once. One’s first impression was that he was a great embodied intellect rather than a human being. [...] I early observed that his abstracted habits, while they kept him as ignorant of the world as he was indifferent to it, did not prevent his occasionally exercising a keen, if fitful, appreciation of character. He would refer to past incidents, which at the time he had not seemed to remark, with a singular, though never uncharitable, insight.”

This combination may have been the main reason the Dublin gossip got so out of hand; De Morgan’s and De Vere’s descriptions clearly allow for a reputation as an eccentric for those who only knew Hamilton from a distance. And Hamilton would sometimes even worsen it when, for instance, he answered, upon having been asked what he had been thinking about, that he was trying to multiply the North-East by the South-West. Famous people are always talked about and, taking into consideration that in those times there were no computers, television or cinema, talking about such a strange man will have made an amusing pastime.

Adding to this eccentric reputation was the way Hamilton wrote about the three women in his life. In his ante-nuptial poems, which he sent to Coleridge and therefore probably also to De Vere and to many more people, he openly wrote about all three women; Catherine Disney, Ellen de Vere, and Helen Bayly, and he gave the associations he had with each of them: Sweet piety, Enthusiasm, and Truth. But regularly almost mathematically examining his thoughts and his feelings, therewith having been able to make his psychological discovery in the summer of 1832, he gave a very logical reason to be so open about the women in his life: he argued that he would have been dishonest then if he now would deny having loved them. He wrote in one of his ante-nuptial poems:

O be it far from me, and from my heart,
Praising a new love to dispraise the old,
As if I had before but false tales told,
In hasty error, or in flattering art!

That he felt that way is easy to understand, he did not lose them because of a relationship with them which went wrong; they were no ‘ex-lovers’. And it completely fits in with De Morgan’s observation that Hamilton would rather “express his opinions to avoid the possibility of being misunderstood.” His then wife-to-be apparently understood that; she knew about his extreme honesty because she already knew him for years from very close-by, and she had seen how difficult it was for him to get over Ellen de Vere. She thus clearly knew all about Hamilton’s former loves yet agreed to marry him; being as honest as he was, gaining her the association Truth, she may have accepted him especially because of his honesty.

But Graves did not recognize Hamilton’s stance towards honesty in regards to the women in his life, just as he had not recognized Hamilton’s psychological change in the summer of 1832, making him lament about Hamilton’s “susceptible heart.” It is uncertain how in Hamilton‘s time this seemingly romantic attitude was judged, but it directly influenced the later gossip when it was concluded, taking Graves literally, that Hamilton had always loved Catherine. Which he did as can be seen in his poem, but not in the way of a secretly nursed only love.

What was, already having such a precarious public reputation, in the end devastating for it was his drinking very openly, even during the times the Temperance Movement was growing. In his younger years Hamilton did not drink at home, and in later years he only sipped porter when becoming tired during some very interesting investigation, but he enjoyed drinking at public events, and he apparently could drink a lot without getting in trouble.

This was shortly alluded to in a 1965 article by John Reid, then acting director at Dunsink Observatory. In the article he first gave the then prevailing opinion, coming directly from Graves as was shown in our gossip article, that Lady Hamilton had not been the strong wife Hamilton had needed, but then, remarkably, he stated that Hamilton had had a “very happy” marriage. When mentioning that Hamilton had not been able to attend the 1840 meeting of the British Association in Glasgow because of the birth of his daughter, Reid writes: “He must have regretted this, since it would have given him an opportunity to meet Encke and Jacobi. On the one occasion on which he did meet the latter [at the 1842 Manchester meeting of the British Association], each of them was left with a deep mutual respect for the other’s drinking prowess.” Hamilton thus was not the only one; gaining a deep mutual respect shows that they drank publicly, and it sounds as if they were very much enjoying themselves. But Jacobi did not have such a bad reputation already, and he was never called alcoholic.

When the Dublin gossip got out of hand Charles Graves visited Hamilton twice to warn him about his reputation. The fact that he had to repeat his warning is a clear sign of what De Vere indeed described, that Hamilton was largely indifferent to the world, that he did not care about his reputation of an eccentric, too honest, openly drinking genius. But he was far from indifferent to the people he loved, and it is a good thing that he did not live to hear about the ever more caricature-like picture sketched of him and of his beloved wife. To which recently was added that he made “attempts at self-harm,” making it an open question what will be added next.*

* Update 2020: The page at IOPblog is removed, I therefore linked to the snapshot at the Wayback Machine. But searching whether or not the remark is repeated, I found the source of the remark in the IOP blogpost through a book review in the Poetry Ireland Trumpet of 2014, of the book by McGovern, A Mystic Dream of 4, from which it was quoted. Unfortunately, the book is not online, and therefore it is not possible to check whether or not the quote is correct.
I could not find a further repetition of the self-harm claim.




Utrecht, 15 June 2018 — Hamilton and Coleridge

Writing the essay I had noticed that Hamilton mentioned several times to have become “a sadder and a wiser man”, and I had assumed that it had been prompted by his romanticism. I had also read Hamilton’s conversation with his sisters, given below, about the ‘Ancient Mariner’, poetry, science, and his tendency or motivation to generalize, and I knew about the deep respect he had for Samuel Taylor Coleridge. But I had totally missed the connection between these three particulars because I had not read Coleridge’s 1798 poem, The Rime of the Ancient Mariner, I did not even know it was written by Coleridge. Perhaps I can be excused; if I had been writing a comprehensive biography I should have done so, but I just focused on countering the negative views on Hamilton’s private life.

Now having read the poem, which can be found on the website of The Poetry Foundation in an 1834 version, the conversation with his sisters [Graves 1882, 345-346], which was in itself already quite clear, again makes more sense. It took place about two years after they had come to live at the observatory, and four and a half year after Catherine’s marriage; a time of which Hamilton later said that he was able to maintain his “philosophic calm” “with lucid intervals indeed.”


“Memorandum by W. R. Hamilton of a conversation.

Monday Evening, November 9, 1829.

After being by myself for some hours in the study, I went to the parlour, where Grace, Eliza, and Sydney were sitting, and entered with them into conversation on the “Ancient Mariner,” which they had been reading. Grace complained that, though there were many beautiful parts in the poem, she did not understand it, and could not believe it to be true. I thought that the moral of the story was the duty of loving all God’s creatures, but that the chief object of the poet was to show the natural in the supernatural, by placing a human being under circumstances contrary to human experience, yet attributing to him feelings which we recognise as true; that is, which we are conscious we should ourselves have if we were placed under the circumstances supposed. This truth of feeling I considered to be the highest truth of poetical composition: I thought that one of the chief advantages of poetry consisted in making us acquainted with our own nature, by exercising our understanding and consciousness in the discernment of truth of this kind. Romances may have such truth, and by it may give exquisite pleasure. Novels and ordinary poetic fiction must combine with this truth the observance of that inferior kind which consists in outward probability the truth of circumstances and incidents, as well of character and feeling. A practised taste comes to be offended by a violation of this outward probability in a novel, but need not be so in a romance, or professedly supernatural poem. Eliza thought that it could be of no use to imagine how we should feel or act in circumstances in which we can never be placed, except so far as all imagination is in some degree useful to the mind. I maintained that, in addition to this general use, there was a special advantage resulting from the experimental knowledge which we derive by putting ourselves in thought under remote and even supernatural circumstances, and observing how we feel, or how we believe that we should be affected. It appeared to me that, as in science, mathematical or physical, we have often come to understand better the near by aiming at the remote; so, in the study of our own minds and feelings, we might improve our practical knowledge by not confining ourselves thereto; might come to know better how we should feel and act under real circumstances, by sometimes placing ourselves in such as cannot be realised.”



Utrecht, 8 June 2018 — Astronomy in 1848; Hamilton’s visit to Parsonstown

A short article or rather sketch was published last week in Zenit called ‘Sterrenkunde in 1848’ (not open access available), translated as Astronomy in 1848 and shown here with permission. In this sketch I gave a description of the visit Hamilton made to Lord Rosse and his Leviathan telescope in 1848, the crossing of the rings of Saturn that year, and the discovery of Hyperion. Although William Lassell gave the moon her name, it was seen from a letter by William Cranch Bond that his son George Phillips Bond was the first astronomer who saw Hyperion. The three astronomers were credited together with finding Hyperion, which is of course fair, but the fact remains that Bond Jr. was the first one to see it.

Just before the visit Hamilton had had a six-week correspondence with Catherine, and had learned from her that from the beginning she had been very unhappy in her marriage, something Hamilton had not known before; he had assumed that the marriage had started out happily as can be seen from an 1825 poem he wrote for her but never sent. He had of course been very distressed by learning that the marriage had been unhappy from the start, and coincidentally only a few days after the last letter, he was invited by Lord Rosse to come to Parsonstown, where he arrived on the 27th of August. In the last week of August, while on his way to Parsonstown and during the first days there, he had a very open and honest correspondence with his friend De Vere, who was able to comfort him. As appears from his other letters written while in Parsonstown, at the time the short sketch of this visit starts Hamilton had calmed down again, always able to enjoy good company and feel ‘the affection of fond friends.’

At some time during his visit, most likely on the 8th of September, Hamilton was teased by Airy for drinking only water. Hamilton had abstained for two years, but as can be seen in his letters without much motivation; he had always been used to, and very much liked, “the pleasures of the table”. He had decided to abstain in an effort to stop the Dublin gossip after a bizarre event in 1846. Hamilton did not believe it was caused by alcohol but by excitement, but Graves had had doubts about what happened then, and assumed that Hamilton might have been drunk. Yet Graves did not live in Ireland then, and his doubts came from the reports he received. To be certain that Hamilton would not further jeopardize his reputation, Charles Graves, brother of the biographer, visited Hamilton and advised him to abstain, which Hamilton did.

Because Hamilton had only abstained to save his reputation, it can be imagined that, enjoying the astronomy and the company, in Parsonstown he concluded that after more than two years he had shown to everyone that he was indeed perfectly able to handle alcohol, as he had always been. Indeed, even in the weeks of distress over Catherine he had not drank alcohol, something he only seems to have done when having a good time with friends, or in the night when trying to finish some work but becoming tired. He then sipped porter, a sweet, dark brown beer which doubtlessy gave some energy due to the sugars it contains. And it must be taken into consideration that in those days nothing was known of the long-time effects of alcohol, what was known was the immediate effect of being drunk, leading to much unpleasantness. But that never happened; perhaps apart from that one time in 1846, also according to Graves Hamilton was never really drunk.

Still in Parsonstown, on the 11th of September 1848 Hamilton wrote that he was going to leave on the 12th, yet many years later he wrote that early in October, while being in Parsonstown, he had received a suicide letter from Catherine. That led Hankins to suggest that Hamilton mixed up the months and had received Catherine’s letter early in September, and he thus concluded that Hamilton, having read the letter, broke his vow of abstinence because of the “internal torture” about Catherine. Which certainly would have been a sign of alcoholism.

But Hamilton had not vowed, and in the essay I showed that he may have stayed in Parsonstown longer than he had planned, making it possible that Catherine’s letter arrived early in October as he mentioned, instead of early in September as Hankins suggested. It would mean that Hamilton drank the champagne long before having received Catherine’s letter, while enjoying his stay; that his ending his period of abstinence thus had nothing to do with her letter.

That Hamilton may have stayed in Parsonstown until the second week of October was inferred from the fact that he wrote letters to Lord and Lady Rosse, according to Graves, ‘soon after he returned home’; these letters were written in the third week of October. A reason for Hamilton to stay will have been the enervating astronomy during those weeks, made possible by Lord Rosse’s Leviathan telescope.

Of course, in the end Hamilton did receive Catherine’s letter. Graves did not mention it although he certainly knew about it, he just did not give any letters written between the 11th of September and the 27th of October. He therefore also did not have to say anything about how Hamilton coped with his feelings when he did receive her letter; it must have been hard.

Having finished the essay and the ‘gossip’ article, I thought it a pity that the cheerfully painted picture, as it emerged from Hamilton’s letters, of how they were doing astronomy in those days, was lost to the alleged drama surrounding Catherine’s letter and the alcohol. That holds for many more good stories and vividly described events in the biography, in most cases because they are coloured by the veils of darkness Graves draped over it. I was therefore happy that the sketch of Hamilton’s visit to Parsonstown was published; a visit which was long forgotten to have had many joyful days also.



Utrecht, 31 March 2018 — De Vere about Hamilton’s affection for his wife

Modified 16 April 2018

Last week the Librarian for Irish Studies of the University of Notre Dame in Indiana very kindly sent me photographs of a letter, written fourteen years after Hamilton’s death by his very good friend Aubrey de Vere, and directed to Hamilton’s later biographer Robert Perceval Graves. I had been allowed already to read the seller’s description of the collection of fifty letters which has been bought by the Library of Notre Dame and to which this letter belongs, but the quote in that description had not been so outspoken as what can be read in this piece of De Vere’s 1879 letter, from which some remarkable conclusions can be drawn.


A part of the first page of an 1879 letter by Aubrey de Vere to Robert Graves


On the 12th of December 1879, fourteen years after Hamilton’s death, his very good friend Aubrey de Vere wrote to his biographer Robert Graves: “The sonnet “Tis Sweet” seems to shew that up to that time, A.D. 1837, Hamilton’s affection for his Wife had not waned. Indeed I do not know that it ever did [...].”*

This is a part of the first page of the letter, which was written three years before the publication of the first volume of the biography. It can be seen that I adjusted the photograph a little at the top.
Reproduced from the original held by the Department of Special Collections of the Hesburgh Libraries of the University of Notre Dame.


A good and happy marriage

To my surprise and happiness, the part of De Vere’s letter shown above contains a strong confirmation of my most important supposition, that the idea that Hamilton had a bad or loveless marriage is not true. The last time Aubrey de Vere** and Hamilton saw each other was in 1863, when Hamilton was quite ill already, and that makes Graves’ remark, that Hamilton “remained to the end of his life an attached husband” [Graves 1885, 335],*** something Graves and De Vere agreed upon.

Since of Lady Hamilton it has never been claimed that she was unhappy having married Hamilton, that in one of the few quotes of her letters she wrote that “his whole happiness seems to be in making others happy; indeed any woman is blessed to be married to such an affectionate kind creature as Hamilton” [Graves 1885, 61],*** and taking into consideration that after both her two long illnesses Hamilton changed his behaviour and their daily life became stable again, it can be concluded that they indeed had a good and happy marriage.

* This letter was written in the Victorian era, in which words as ‘affection’ and ’attachment’ were generally used to indicate loving spouses and good marriages.

** De Vere wrote his name as we do in the Netherlands: when writing his full name he wrote his insertion with a lower case letter, ‘Aubrey de Vere’, see his Recollections or a hand-written letter. Because De Vere’s father wrote about his wife as ‘Lady De Vere’ [Graves 1885, 235], in my essay I assumed that also Aubrey de Vere would write his name, in case his given name was not used, as ‘Mr. De Vere’ or simply ‘De Vere’, and since that is exactly how we do it I listed him under ‘V’: ‘Vere, Aubrey de’.

*** It is impossible to give positive remarks made by Graves about the Hamilton marriage which are not embedded in the criticisms discussed in our ‘gossip article’; these criticisms having been needed, as he doubtlessly believed, in his efforts to counteract the Dublin gossip. Still, however critical he was about how the Hamiltons lived their daily life, Graves never said that the marriage was unhappy. For a discussion of the context of this remark see [Van Weerden 2017, 168-169].


Aubrey de Vere

Also striking is the continuation of De Vere’s sentence which reads: “or that [Hamilton] ever discovered how little she approached to his early ideal of her.”* Because it is hardly conceivable that Hamilton would not know his wife after more than thirty years of marriage, this rather seems to shed a light on De Vere himself. When it is taken into account that they lived in a time in which the inner pleasures and struggles of marriage were hardly talked about, it could be surmised that because De Vere never married he did not realize that what he remarked is almost impossible.

De Vere seems to have been a very kind, serious, thoughtful and deeply religious man, although he could also be ironic [Graves 1885, 201-202], politically indignant [De Vere 1848], and sometimes really funny [Graves 1882, 613]. In 1855, two years after Catherine Disney’s death, he had an intense correspondence with Hamilton about her, in which he was able to give Hamilton much consolation. But not having had a very good understanding about the ups and downs of every marriage would explain why De Vere sometimes reacted so philosophically on Hamilton’s outpourings. For instance, towards the end of that correspondence, after Hamilton had called Catherine Disney a “Beautiful Vision”, De Vere philosophized that “all such Visions should be looked on as Anticipations and Types of the Glory and Beauty unrevealed, rather than as lights which have melted away into the sad shadow-land of the Past” [Van Weerden 2017, 313]. It had “almost tempted” Hamilton “into writing again on the potentialities of the past,” but he apparently realized that he had to stop before he would jeopardize his marriage.** Writing for some months in such opennes had done him good, but continuing to do so would be harmful; he loved his family. De Vere mainly saw the romance in it all.

How very theoretically or perhaps theologically De Vere regarded marriage can, I think, be seen in his poem ‘The Infant Bridal’ [De Vere 1855]. I was a bit shocked when in this poem a marriage which was arranged between two royal children in order to achieve peace between two kingdoms turns out to be extremely happy. Through their Christian faith, or everyone’s, the children almost instantaneously loved each other, and the marriage was consummated after the boy came back from war as a victor over heathens and had become a man. Assuming that the boy had changed after having seen the horrors of the battlefield, where indeed many men died, I expected trouble, but the couple turned out to be so happy that the whole country was blessed. Although in the last stanza De Vere suggests that a “profane and unbelieving crowd” might not go along with this story, he asks them why such a marriage could not be blessed by God if it brought with it peace for two kingdoms. In his days, when marriage was regarded as holy, people may have found it a beautiful and heartening poem, but it is hard to accept today.

The suggestion that De Vere had a higly theoretical view on marriage is also in agreement with the notion that he does not seem to have realized that Hamilton’s idea of an ideal wife was different from his [Van Weerden 2017, 105]. In the essay I have argued that Hamilton did not search for a literary, poetical and sophisticated woman, which was clearly an ideal of both Graves and De Vere who, much more than Hamilton, lived in highly educated upper class circles. Apparently realizing what his intense way of working would ask from a wife Hamilton was searching for a pious, truthful and almost reclusive woman,*** and Helen Bayly deeply was and remained to be the woman he supposed her to be “after a long continued and long impartial study” he had made of her character before asking her to marry him; they had known each other for years already.

But even in case De Vere was right after all: how happy a marriage must be in which one never discovers that one’s partner is not the ideal person one fell in love with in the first place.

* After seeing the photograph of the letter containing this part of the sentence on the internet I decided to take the sentence off; to prevent new gossip it clearly needs the context in which De Vere wrote it, and of who De Vere was.

** Hamilton did not just force himself to stop and hide his true feelings as this might suggest; already in the summer of 1832 he had discovered how bad it was for him to keep reminiscing about “incidents of the past” as he had done then already for so many years, first about Catherine Disney and then about Ellen de Vere [Van Weerden 2017, 118]. That summer Hamilton realized that he had led a “passion-wasted life” and risked never to fulfill his boyhood dreams of fame, upon which he made a very succesful effort to change that by stopping to lose himself in melancholic reminiscences. An effort which, as Hamilton wrote to De Vere, led to a “revival” of “the power of hope”, and in the weeks following this discovery this power of hope began to show “its effect in restoring [his] tone of mind and even [his] health of body.” And, as I assumed in the essay, to finding conical refraction in October and and falling in love with Helen Bayly in November. It was not just that year that he succeeded; many years later he still referred to this important discovery. It is not known why neither Graves nor De Vere recognized or acknowledged this change in Hamilton although motives can be guessed: De Vere missed the poetry, and Graves clearly believed that Hamilton should have tried harder to win Ellen de Vere. Which in turn was not a good idea in De Vere’s eyes; indeed many people had an opinion about how Hamilton should have lived his life.

*** Lady Hamilton was reclusive in the sense of not wanting to go into society, but she did have very many relatives and throughout the biography it can be seen that she visited them and they visited her; visits which often lasted for several days. Being reclusive certainly did not mean wanting to be alone.


The poem ‘Tis sweet’

De Vere’s letter contains another remarkability. The sentence in the photograph starts with referring to an 1837 sonnet: “The sonnet ‘Tis sweet’ seems to shew that up to that time, A.D. 1837, Hamilton’s affection for his wife had not waned.” It is indeed surprising that De Vere associates this poem, which was written on 16 June 1837, with Lady Hamilton, because in his biography Graves had associated the poem with De Vere.

Since the summer of 1836 Lady Hamilton’s mother, Mrs Bayly, had been very ill, and in order to care for her Lady Hamilton was in Nenagh with the children. Hamilton visited them regularly and for long periods of time, but in April 1837 he had to go to Dublin for various obligations. Shortly before he could return to his family in Nenagh De Vere made a ten-day visit to him at the Observatory, during which they walked together, visited many places and enjoyed the Dargle river and the Powerscourt Waterfall. Graves gave four sonnets as inspired by this visit, and remarked that Hamilton had sent them to De Vere. He then comments: “One of these was addressed to his wife, in the prospect of his again joining her and his children and her mother; the others recorded the pleasures of his renewed association with his friend” [Graves 1885, 198]. The third sonnet, starting with ‘Long time, O Lady mine and truest Wife!’, was obviously addressed to Hamilton’s wife, which means that according to Graves the fourth sonnet, ‘Tis sweet’, belonged to “the others”.

The sonnet was written shortly before Hamilton could return to Nenagh after two months of separation, and he had missed his wife and children terribly.

‘Tis sweet when joy, that has been long away,
Re-visits us with unforgetting smile,
And whispers that in all that tedious while
It only seemed from our sides to stray;
When after dreary months, a sudden May
Woos us abroad, with many a loving wile;
Or when we listen in cathedral aisle
An anthem that we heard some long-gone day;
Or gaze on face of some long-parted friend.
Or scene that we had gazed on long ago;
Or feel within ourselves the subtle flow
Of some remember’d mood steal on, and blend,
In union fine, old thoughts and new; or pore
On some delightful page, long read before.
June 16, 1837.

Having read De Vere’s letter and therefore knowing that according to him the poem was about Lady Hamilton, also De Vere’s comments in the biography make more sense. The second sonnet, starting with ‘Shall we not long remember, Friend beloved!’, was clearly addressed to him, and after having received the sonnets he wrote to Hamilton: “Do you know I can hardly look back upon a time of greater enjoyment than those ten days we passed together? It is very seldom indeed that anything thrown so little back into the distance of imaginative memory affects me in the same sort of way; and your four Sonnets* will assist, not in keeping up, but in deepening, this feeling. Your last,** by the way, is becoming a great favourite with me, and my mother seems to like it the best of all: my father, too, is delighted with all of them; but, for my part, I am not prepared to give up my partiality for that peculiarly addressed to me. I think them decidedly the best Sonnets you have written” [Graves 1885, 200].

The last part of this quote seemed puzzling when accepting Graves’ remark that the last sonnet was about seeing De Vere again, not only because it would be quite intimate for a Victorian friendship, but also because it was becoming a favourite and if it had also been addressed to him De Vere would not have had to give up his partiality. Having connected the last sonnet, ‘Tis Sweet’, to Lady Hamilton in 1879 he may also have done that in 1837 already; not all De Vere’s letters have been given by Graves in their entirety. But had Hamilton in any way suggested that the poem had been about their friendship after all, De Vere would have remembered that when he wrote his letter to Graves.

It is often difficult to comprehend why Graves was so negative about Lady Hamilton that he rather assumed that this sonnet was about the in his eyes beautiful friendship between Hamilton and De Vere, until it is called to mind again that he was trying mightily to counteract the very bad gossip in Dublin; the friendship with such a refined poet would shine brightly on Hamilton’s remembrance. And Graves could not know how many years thereafter people still would read his biography, knowing nothing about the gossip.

* Graves mentions five sonnets as inspired by the visit, but the fifth was written after De Vere’s reply to Hamilton in reaction to the four earlier poems.

** Italics by De Vere.


Poetry

In the essay I showed that Wordsworth and De Vere rated Hamilton’s poetry much higher than Graves did. Graves was of course not such an accomplished poet as Wordsworth and De Vere were, and for Graves Wordsworth’s criticisms seem to have been a sign that Hamilton’s poetry was not always so good. Or, to see it a bit more positively, he may have found it difficult to give poems which in his eyes still should have been worked on before publication.

That Hamilton’s poems often needed more refinement was indeed Wordsworth’s opinion, but he never said that Hamilton wrote bad poetry or could not become a good poet. Most of the biographical sketches follow Graves’ very critical opinion about Hamilton’s poetry, but carefully reading the original letters, also given by Graves, shows that what Wordsworth said was that he did not want Hamilton to spend much time on the minutiae of words and phrases in order to become a good poet, at the cost of his mathematics in which he could reach the absolute highest goals. And he did not only say about Hamilton’s poetry that it needed more work although it did need more than that of his sister Eliza Hamilton [Graves 1882, 268, 385], something Wordsworth said explicitly about her poem ‘The Boy‘s School’ [Graves 1882, 682] which she therefore may have adapted before publishing; Wordsworth said that every poet has to do that, and that he could point out “five hundred passages in Milton upon which labour has been bestowed, and twice five hundred more to which additional labour would have been serviceable: not that I regret the absence of such labour, because no poem contains more proofs of skill acquired by practice” [Graves 1882, 492].

Indeed, next to being critical, Wordsworth was remarkably complimentary; after giving some criticisms to the poem ‘The Enthusiast’ he wrote to Hamilton: “After having directed your attention to these minutiæ, I can say, without scruple, that the verses are highly spirited, and interesting and poetical. The change of character they describe is an object of instructive contemplation, and the whole executed with feeling” [Graves 1882, 326].

De Vere was even more impressed, writing in 1832 that “I constantly read your poems with my Æolian harp in the window; the unison of sound and song has often brought back scenes before my eyes with strange distinctness.” And in his 1879 letter to Graves he continued the letter writing: “I suppose if [Hamilton] had not married [Helen Bayly in 1833] that remarkable out burst of poetry which characterized the year 1832 would have continued, & left large & important poetical results behind it.* Wordsworth used to call Coleridge’s 26th year his Annus Mirabilis. In some respects I think Hamilton’s 27th year might be so termed.”

Next to being again very complimentary and thereby contradicting the often proclaimed simple judgement that Hamilton wrote bad poetry, what De Vere seems to have missed here was that the end of this outburst of poetry came already before Hamilton fell in love with Helen Bayly; it was a direct consequence of Hamilton’s aforementioned discovery in the summer of 1832. In agreement with the picture of De Vere sketched above, after Hamilton had told him that he had discovered that he had led a “passion-wasted life”, which was the onset to his change and the ‘revival of the power of hope,’ De Vere seems to have taken the expression “passion-wasted” a bit too general or theoretical, writing to Hamilton, “I cannot bear that expression “passion-wasted life”. Is not passion the most essential means by which our souls are purified and elevated?” The bachelor he was, he apparently did not recognise how strongly Hamilton’s poetry from that in his eyes remarkable year was connected to deep unhappiness after losing Ellen de Vere, or, the poet he was, he did not consider unhappiness too unpleasant if it led to beautiful poetry. But while De Vere wanted poetry, Hamilton wanted to have a family life, and although with his marriage his “remarkable out burst of poetry” came to an end, he found the life he had longed for.

* From the letter given by Graves it seems clear that De Vere hoped that these four sonnets would be the start of a new outburst of poetry; he continued his earlier mentioned sentence that the 1837 sonnets were “decidedly the best Sonnets you have written” by writing: “and I am not at all surprised at this. We constantly succeed particularly well in what we have not practised for some time. I hope you will keep your half-promise and go on writing. We should always get as much as we can out of those unaccountable fits of spontaneity which come upon us now and then, at least enough to illustrate the mood we are in, and the degree of development we have reached, so as to note the progress we have made” [Graves 1885, 200]. This shows, by the way, that Hamilton could also write in De Vere’s eyes beautiful poetry when inspired by happy feelings. But Hamilton found it difficult to work when his wife was not around, and finally reunited with her, the flow of poetry had to make place again for the flows of mathematics he had become famous for.



Utrecht, 11 February 2018 — The siblings of Hamilton’s father, and the Rowan name

The handwritten Dublin church records are appearing online, and searching the records can lead to surprises. According to Graves’ family tree, [Graves 1882, xix], Hamilton’s grandparents William Hamilton and Grace Hamilton MacFerrand had five sons and a daughter. Of four sons the baptism records were found; they were baptised in the parish of St. Mary, and in the record of the eldest child, Arthur, who was born in 1775, their address is given as Jervis Street. That was were, according to Graves, they lived indeed [Graves 1882, 6]. One surprise was to see that William, one of the three sons who, according to Graves, died early, was a twin brother of uncle James. Strangely enough, in all three baptism records (of four sons) it can be seen that the entries are inserted later.

Hamilton’s grandmother, Grace MacFerrand, was Scottish, and she was an adopted sister of the famous Archibald Hamilton of Killyleagh Castle, who had added to his name his mother’s last name Rowan. From the records it appeared, again surprisingly, that two sons of William and Grace were named after Archibald Hamilton Rowan: next to what was known, that Hamilton’s father was called Archibald after him, their eldest son was called Arthur Rowan, and that was not known. In his biography Graves mentions that Archibald Hamilton Rowan was Hamilton’s godfather, which explains Hamilton’s second name Rowan. The fact that three Hamilton boys were named after Archibald Hamilton Rowan, namely Hamilton, his father and his uncle, seems to indicate very close bonds but that was only through Grace; Hamilton’s father Archibald explicitly mentioned that he was not related to the Hamiltons of Killyleagh Castle.

For an overview and links to records and relevant passages in Graves’ biography (including an example of how Graves could let his readers feel his contempt for someone using only parts of sentences) see The Hamiltons of Jervis Street and the name Rowan.

Note added later: An apparently very good overview of the Hamilton family of Killyleagh Castle, from an ancestor Archibald Hamilton in 1536 up to James Hans Hamilton at whose house, Abbottstown, Hamilton and his children “enjoyed” on the last evening of 1851 “a sort of Christmas festivity” [Graves 1889, 311], and their connection (not family relation) with the Dublin Hamiltons, has been given by Gary McGuire: The curious connection between William Rowan Hamilton and other Hamiltons.

There are things left to investigate. It does not seem to be known which son of William and Grace Hamilton died, apparently still rather young, in a French prison. There are two burial records, one from the 28th of February 1779 and one from the 8th of May 1784, of ‘Wm. Hamilton’s’ and ‘Mrs. Hamilton’s’ child in Jervis Street respectively, but no names are given. The eldest son, Arthur, having been born in 1775, these two must have been young children indeed, leaving one brother to join the army. In the pdf about Hamilton’s name Rowan I have argued that that will have been Arthur.

And there is a letter, mentioned by Graves, sent by Archibald Hamilton Rowan to Hamilton. According to Graves, in this letter Archibald Hamilton Rowan congratulated Hamilton with his knighthood, which is a problem because Hamilton was knighted in 1835, and Archibald Hamilton Rowan seems to have died in 1834, see the burial record of Archibald Hamilton Rowan. Therefore, either there were two Archibald Hamilton Rowans, or this is a riddle which could perhaps be solved by reading the letter, which should still be in Trinity Library.

Note added later (2018 or 2019): On the 3rd of March 1834 Sarah Anne Hamilton Rowan was buried, see the burial record of Sarah Hamilton Rowan. As her address Holles Street was given, exactly the same as in Archibald Rowan’s burial record. That seems to end any doubt whether the burial record of Archibald Hamilton Rowan was that of -the- Archibald Hamilton Rowan, which makes the letter even more intriguing: who wrote this letter, or where did Graves go wrong?

Note added December 2020: I have revised the pdf about Hamilton’s name Rowan. I extended the part about the siblings of Uncle James and Hamilton’s father, and added a supposition about Arthur Rowan, the eldest brother, who “died in a French prison.”



Utrecht, 4 February 2018 — Patrick Wayman, our gossip article, and the “fabrication, or at any rate a gross exaggeration” of the uneaten meals in Hamilton’s study

Some days ago I reread our gossip article. Apparently having become blind to the text, I realize now that something was not mentioned which should have been mentioned, namely that in William Edwin’s story about the chops the plates were not between the papers as Macfarlane wote; the nephew, John Garnett Rathborne (1820-1895), who was a very good friend of Robert Stawell Ball [Van Weerden 2017, 359 footnote 62], said that he saw the plates on top of the piles of papers.

In his book about Dunsink Observatory (not available online but for loan in many libraries as can be seen in the WorldCat; Dunsink Observatory), Patrick Wayman drew attention to this twist of history writing: “The ultimate tale is told of the uneaten meals that were found sandwiched between papers in [Hamilton’s] study after his death, but it seems that this story was a fabrication, or at any rate a gross exaggeration.” It is unfortunate that in the article we did not give him the credits for emphasizing this so strongly that it triggered us to search for the original texts, which in turn made it possible to write the second part of the article.

It would indeed be difficult to imagine that Hamilton, for whom letters and papers were very important, would do something like putting papers on a plate. When he laid a letter aside, it was in order to answer it later, but that also held for following letters, which he received in abundance from family and friends, from fellow scientists and members of the public. He often answered very soon, unless when he was in one of his mathematical ‘incubation periods’. The many letters temporarily laid aside to be answered later will then have mixed with all the interesting books and articles laid aside to be read and used later.

But it is actually not so strange as it sounds; if suddenly the contents of our computers, supplemented with the articles and books we added to our reference lists to read or use later, would be strewn about in paper form most of us would be shocked by their accumulated volume. There is the famous photograph of Einstein’s paper covered desk; that happened even though he had the assistance of Helen Dukas, his full-time secretary, while the only assistance Hamilton had was, every now and then, from Thompson (who was of course not a secretary but the astronomy assistant, and did most of the observatory work during Hamilton’s time), and for some years his children who helped with correspondences and texts. And writing his mathematics as fast as another would write notes of invitations, as De Vere once remarked, Hamilton will also simply have produced more paper than others did.



Utrecht, 2 February 2018 — Macfarlane, William Edwin Hamilton, alcohol, gossip, history in need of corrections in case of new insights

About two years ago I found an article, written by Alexander Macfarlane in 1902, about William Edwin Hamilton. William Edwin had just died, and Macfalane wrote a sort of obituary in Science Jan-June 1902, see also [Van Weerden 2017, 10.8]. In the essay I gave it in its entirety because of its strangeness; it is overall very denigrating. That kept me thinking and wondering, what would motivate a man to write such an article, in a very renowned journal, for the world to read. It is reminiscent of Graves’ about six critical pages in Hamilton’s biography, but Graves certainly did not go so far. Although Graves did have a very negative opinion about William Edwin, even writing to Ellen O’Brien de Vere that he did not have a moral principle, Graves did not mention that in the biography.

Augustus Bridle (1868-1952, Historica Canada), described William Edwin during his apparently most alcoholic period in his 1924 Hansen : A Novel of Canadianization, but he called William Edwin ‘Burnham’, and Chatham ‘Plainsville’. If it had not been for Victor Lauriston (1881-1973, Historica Canada), who in 1952, in an article in the Chatham Daily Planet which was given by Patrick Wayman in his Dunsink Observatory, 1785-1985, mentioned that Bridle had described William Edwin, no-one would have known that anymore. And even though Bridle describes him in his drunkenness and poverty, and with the according to Bridle sad futility of his enormous knowledge, he portraits William Edwin as a ‘kindly old Irishman’ citing Latin verses and addicted to speeches in Greek. It therefore remains understandable why he was known in Chatham for his literacy and was a member of the Macaulay Club, according to Lauriston “the oldest literary and debating club in Canada.”

Lauriston’s and Bridle’s descriptions, direct and without embellishment but with a hint of admiration, makes Macfarlane’s article clearly different. Where, for instance, Bridle and Lauriston wrote that William Edwin slept on a “straw pallet in a room behind the law offices,” Macfarlane wrote that his “sleeping place was said to be the loft of a livery stable.” And it may be true that William Edwin wrote ‘doggerel’ verses as Macfarlane states in his article, but he never pretended anything else [Peeps 1895, 9], which means that it did not have to be discussed. The article therefore seems to be following Graves’ opinion, but sounds much harsher by its compactness and without all Graves’ nuances, just as in case of the lecture about Hamilton Sr., where Macfarlane followed Graves’ opinion but wielded a very different tone.

Macfarlane retired to Chatham in 1898, and although he must have seen him earlier, he will have known William Edwin only for his last four years. In those years William Edwin had already published his Peeps, and most likely hardly drank alcohol anymore, which can also be deduced from Macfarlane’s article. At that time Macfarlane lectured about Hamilton Sr, and in 1904 he published a Bibliography of Quaternions in which William Edwin is named because he was the editor of his father’s posthumously published Elements. Macfarlane must therefore have been very aware of William Edwin’s presence in Chatham. About both Hamiltons he emphasizes their use of alcohol, and in our ‘gossip’ article his lecture about Hamilton Sr. is indeed part of the chain of biographical sketches leading to Hamilton Sr.’s contemporary alcoholic image. But the question is why.

Perhaps Macfarlane wanted to show that Hamilton Sr. really misused alcohol because his son did. Or due to the son he started to believe that the gossip about the father must have been true. But that still is no explanation about why he thought he should publish his opinions about the Hamiltons in the way he did. Assuming that he did not simply want to wage a vendetta against the Hamiltons, or was jealous, which I feel would be a cheap explanation, was it about alcohol and temperance? Or did it have to do with the Victorian era? And if so, what? There does not seem to be a biography about Macfarlane, in which possible answers could be found.

The question is as intriguing as the question why Graves chose to blame Lady Hamilton instead of following Hamilton’s own opinions. But it would doubtlessly take a study of their own papers to gain an understanding of their motives, and a lot of time. Unfortunately, I do not have nine lives. Since in those days temperance was also widespread in Canada, for now I would vote for the temperance argument until it was shown that Macfarlane did drink alcohol. To what his motivation may have been then I have no clue. Prohibition was for many years sought after by a majority of the people; it occurred in Ontario in 1916 but was repealed again in 1916 (in Ireland the temperance movement was already strong in 1840). If Macfarlane indeed abstained, he may have used the Hamiltons as examples of how bad alcohol is for everyone.

In any case, the suggestion seems to be fair that, after drinking became socially accepted again, historians ‘forgot’ to restore the reputations of those who had not complied to the views of the majorities around them and remained to drink als most people did before and after those periods. Which conserved the ruined reputations of both father and son Hamilton. And, of course, of Lady Hamilton.



Utrecht, 29 January 2018 — Ellen de Vere, Miss Ellis of Abbotstown, and parents bereaved of nearly all their children

It is unfortunate that in a biography so large as that of Graves things tend to get overlooked; when starting to read the biography some time is needed to get aqcuainted with everyone. What I overlooked is that Hamilton first saw Ellen de Vere in 1829 when she was visiting her friend Miss Ellis of Abbotstown. Perhaps, but Hamilton was not sure, it was during Wordsworth’s visit to the Observatory, when Wordsworth and Hamilton dined with the Ellis family [Graves 1882, 470].

Ellen de Vere had been “a most intimate friend” of Miss Ellis, who died in 1830. In 1832 Hamilton wrote a poem starting with the words ‘Was it a dream?’, in which he mentions both Miss Ellis and Ellen de Vere [Graves 1882, 562]. In the poem he contemplates the possibility that if, in 1829, he had not still been brooding over the loss of Catherine while being in the company of Miss Ellis and Ellen de Vere, and would have “sooner known and earlier loved, Her heart’s fine tendrils might have twined around him”; but now it was too late. Hamilton wrote the poem in May 1832 while often very melancholic about Ellen de Vere’s rejection, and therefore it may have been the start of the contemplations leading to his psychological discovery that summer [Van Weerden 2017, 4.3].

After the death of Miss Ellis Hamilton wrote a poem called ‘Easter Morning’ [Graves 1882, 379], a poem which Wordsworth called ‘elegant’, and in which Hamilton described how they heard, and how he felt, about the death of Miss Ellis.

While writing the essay not realizing that she had been a friend of Ellen de Vere it had been the heartbreaking sentence Hamilton wrote about her parents which lingered in my mind for a very long time because of the utter sadness, and because it was, as I felt, exemplary for the very bad medical circumstances of those days. He wrote to Wordsworth: “You remember, probably, our walk through Mr. Ellis’s grounds, and our dining together at his table; and your heart is too full of exercised humanity not to feel some concern on being told that Miss Ellis, who sat next me at dinner, and was even then unwell, has since fallen into a decided decline, which leaves little hope of her escaping a fate that has already bereaved her parents of nearly all their children” [Graves 1882, 355].



Utrecht, 12 January 2018 — Hamilton’s “splendid meteor”

It is common knowledge that Hamilton, although he was Royal Astronomer of Ireland, was not an enthusiastic practical astronomer. That does not mean however that he did not know about astronomy, but that his work was mathematical rather than practical. He could be very enthusiastic about special astronomical events such as eclipses and comets, and seeing the reappearance of the rings of Saturn in 1848. Still, he would hardly have guessed that, after having seen a beautiful meteor, the short notice he sent to a local newspaper would turn out to be the first ever report of a meteor of a complex of radiants.
The article containing his report is published in WGN, Journal of the International Meteor Organization. Since WGN is not open access, the article can be read here, On an 1850 report of a fireball from the Scorpiid-Sagittariid Complex. The abstract reads: “In the night of 13-14 May 1850 both Sir William Rowan Hamilton and his son William Edwin saw a meteor which was “many degrees more brilliant than Jupiter.” This meteor has now been recognized as a member of the so-called Scorpiid-Sagittariid Complex. It makes the report the earliest one of this complex, the hitherto earliest one stemming from 1878.”


Hamilton’s meteor


Hamilton’s 1850 meteor

This picture, representing the path of Hamilton’s meteor, is made with the free planetarium program Stellarium. Clicking on the picture shows a larger size. The three circles represent the path of the meteor: the rightmost circle represents its point of greatest brightness as given by Hamilton, the middle circle its derived starting point, the leftmost circle the theoretical radiant, which is in Ophiuchus. The apparent curvature of the path is a consequence of the curved coordinate system showing azimuth and altitude. The field of view has been chosen in such a way that also Scorpius and Sagittarius could be seen, and that Hamilton’s local horizon would be represented by a horizontal line, making it easy to imagine how he must have seen the meteor. Looking to the south, west is to the right, north is up. Jupiter, to which Hamilton was looking when the meteor appeared, is outside this picture, just having passed the west-southwest.




Utrecht, 7 January 2018 — Lady Wilde, and her son Oscar having been born on the birthday of the quaternions

Lady Wilde (1821-1896), the famous Irish poet Speranza, was held in very high esteem by Hamilton. He clearly regarded her as a friend: in April 1858 he held what he called a ‘Feast of the Poets’ at the Observatory with Aubrey de Vere, John Anster, Denis Florence MacCarthy, and Mrs. Wilde (she would become Lady Wilde in 1864). Aubrey de Vere afterwards wrote about it as “the pleasant day we had with you: our merry dinner, rambles about the green fields, and poetical recitations.” According to Graves MacCarthy wrote “a longer and fervid outpouring” but unfortunately, he preferred only to give De Vere’s “sufficient reminiscence”. [Graves 1889, 604], [Graves 1889, 97-98].

On the 4th of May 1855 Hamilton wrote about her in a cheerful letter to Augustus De Morgan: “A very odd and original lady [...] had also lately a baby: such things you know will happen, at least in Ireland; and on my being asked to hand her in to dinner, at a party given by Colonel and Mrs. Larcom in this neighbourhood, when I met her for the first time in my life, she told me of this “young pagan,” as she called him (or it, for I did not know the sex. I don’t call newborn infants in these countries pagans); and she asked me to be a godfather, perhaps because I was so to a grandson of Wordsworth the Poet [...], and because she is an admirer of Wordsworth. However, I declined. But it seems that I have not fallen entirely out of favour thereby, for she paid me, on Saturday last, a visit of three hours and a-half, it being my second time of seeing her. You must observe, however, that I had made it a sort of open day [to show the Observatory and the telescopes to members of the public], and had several other guests, including a troop of deaf and dumb boys, for whom, and for the others, Lady Hamilton, though prevented by a heavy cold from being disposed to appear herself, had laid out a comfortable luncheon, and allowed her daughter to be present. My visitress told me, as we drank a glass of wine to the health of her child, that he had been christened on the previous day, by a long baptismal name, or string of names, the two first of which are Oscar and Fingal! the third and fourth sounding to me as a tremendous descent, but I daresay she prefers them. You must know that I have been long acquainted with her husband, as a Member of the Royal Irish Academy, though he had not time to come with his wife, on her long and entertaining visit of the other day. She is quite a genius, and thoroughly aware of it. One thing she said, as I was conducting her upstairs to the Dome, and while she was professing to admire the house (which she hoped was a haunted one — my sister believed it to be so), was: “Let a woman be as clever as she may, there is no prize like this for her!”” [Graves 1889, 496-497].

It does not sound as if Hamilton knew, when he declined to become godfather, that Oscar was born on the 16th of October 1854, on the eleventh birthday of the quaternions (as Hamilton called the day of discovery); he most likely would have made a remark about that. Since dates were important to him it can be wondered whether he would have decided differently had he known it, and it is interesting to ponder on the question what would have happened if he would have accepted, or on whether it would have changed anything in Oscar Wilde’s life.

Note: According to the Dublin church records Oscar Wilde was baptized on the 26th of April 1855 in the parish of St. Mark as Oscar Fingal O’Fflahertie Wilde: handwritten baptism record of Oscar Wilde (fifth from the top). Different from what can often be read, O’Fflahertie is written with double f of which the first one is capitalized. Hamilton mentions four names while the baptism record shows only three, judging from the remarks however it seems that four was indeed Mrs Wilde’s intention. According to Hamilton, or Mrs Wilde, Oscar was baptized on Friday, which would have been the 27th of April; in the record it is written that it was the 26th, which was a Thursday.



Utrecht, 21 December 2017 — Hamilton’s formulation of geometrical optics as the marriage between the wave theory of Fresnel and the ray method of Newton

When I was writing the essay, I was happy to recognize Hamilton’s remarkable psychological discovery in the summer of 1832,* for which he was doubly ‘rewarded’: he discovered conical refraction which earned him a knighthood, and fell in love with Helen Bayly which gave him his marriage. For me, being occupied with Hamilton’s ‘defense’ regarding the gossip about his private life, the psychological discovery was far more important than his mathematical discovery. I did know of course that Hamilton was knighted because of conical refraction; as far as is known it was the first time mathematics predicted something which experiment then verified instead of the other way around.

But I had no further thoughts about conical refraction itself, other than that it was some byproduct in optics on the way to what I did understand to matter, Hamiltonian dynamics. That only changed when I stumbled on this website: Hamilton’s Diabolical Legacy by Mike Jeffrey, who gives a very clear introduction to what Hamilton actually discovered, making me finally see (as far as I can understand it) (and after some very kind and explanatory emails) why anyone would think it worth a knighthood. And, by the way, why it also made Humphrey Lloyd famous; he did not ‘just’ provide the experimental proofs. Hamilton had predicted polarization in internal conical refraction, Lloyd saw that polarization also occurs in external conical refraction and explained it using an analogous treatment to Hamilton’s, therewith showing his deep theoretical and experimental understanding of the phenomenon.

Hamilton had started his theory on optics already in his teens; in 1825 he presented his first paper ‘Memoir On Caustics’. It was rejected because the discussions were too abstract, and the formulæ too general, but it seems easy to surmise from the rest of his work that he had found the characteristic function already. Hamilton kept working on it, writing an ‘Essay on the Theory of Systems of Rays’ followed by three supplements, and it was in 1832, during the writing of the ‘Third Supplement’, that he made his mathematical and psychological discoveries.

To my amazement, since this claim was completely new to me, on his website Jeffrey states that “Hamilton’s formulation of geometrical optics married the wave theory of Fresnel with the ray method of Newton. Describing light rays as the normals to level surfaces of some characteristic function, the theory was first published in 1828.” Jeffrey writes about the discovery of conical refraction that in October 1832 “William Rowan Hamilton [...] predicted a singularity, a point where light’s deterministic journey through a simple crystal broke down. The calamity would be observable within Fresnel’s theory of double refraction, seen as a single ray exploding into infinitely many rays, neatly arranged a brilliant cone. In one stroke, the field of singular optics was born and a sensation began that would take 173 years to run its course. Despite prompt experimental confirmation of Hamilton’s beautiful mathematical theory, the phenomenon was long hindered by controversy and misconception. Victorian mathematics contained only the initial sparks of the asymptotic techniques which would be needed to achieve a full understanding.”

Jeffrey then describes how in the course of years many intricacies about conical refraction were discovered, until in 2004 “the first detailed explanation of the conical diffraction phenomenon was achieved by Berry, both qualitative and quantitative, [...] and all aspects of the biaxial phenomenon thus far observed were explained.” What Jeffrey through his PhD thesis added was the effect of chirality (the crystal not being symmetric) on the phenomenon of conical diffraction, and dichroism (not equally absorbing all components of light).

It does not seem to be known whether Hamilton ever contemplated direct applications of this discovery. He made his discoveries in a time in which the very first trains appeared but most of the travelling was done using horses, and he was writing by candlelight in a room warmed by a hearthfire. Therefore, like about his quaternions, which are now used in for instance gaming and space travel, also about conical refraction he could not have guessed what it would be used for today, enhancing holographic applications or the focus of lasers.

* See for a description of the process leading to that discovery [Van Weerden 2017, 4.3, 4.4].



Utrecht, 12 December 2017 — Publication of ‘A most gossiped about genius: Sir William Rowan Hamilton’

Today we received the message that the article which I wrote together with Steven Wepster and which was accepted by the BSHM Bulletin: Journal of the British Society for the History of Mathematics has been published online: A most gossiped about genius: Sir William Rowan Hamilton. The abstract reads: “The Irish mathematician Sir William Rowan Hamilton (1805–65) is often portrayed as an unhappily married alcoholic. We show how this image originated in the 1840s, caused by a combination of the strict social rules of the Victorian era and the then changing drinking habits in Ireland. In the 1880s Hamilton’s biographer Graves tried to restore Hamilton’s reputation by blaming Lady Hamilton for her husband’s habits. This unintentionally caused his biography to become the basis of Hamilton’s overall negative image. We argue for a far more positive description of Hamilton’s private life. Thereafter we trace the evolution of the negative image using an anecdote about Hamilton’s work habits and its increasingly distorted representations.”

We did not try to find all the biographical sketches through the years, instead we chose six well-known books to show how the gossip evolved. In that way we were able to show how through the years the authors built on earlier biographical sketches without reading them carefully or checking original sources for the strongest claims, which led to an evolution of the gossip which resembles the children’s game where a story is passed on by whispering it in the next child’s ear. It led to the contemporary caricature-like image of Hamilton, for instance to the notion that he was an alcoholic for the last third of his life. Graves’ suggestion that Hamilton “craved for alcohol”, an opinion of which we show that it was embedded in his times, was, without Graves’ many nuances, repeated by Macfarlane. It led E.T. Bell, in his 1937 quite gossipy book Men of Mathematics, to depict Hamilton as an alcoholic. It was an image which would cling to Hamilton up to this day.



Utrecht, 22 November 2017 — Publication of the corrected version of ‘A Victorian Marriage’

I uploaded the corrected versions of the pdf and the epub to my website, and the essay also to Google Books, A Victorian Marriage. I rather like the word cloud they made: Lady Hamilton has a prominent place in it.



Babberich, 26 August 2017 — The death of Edward Senior in 1865, most likely the second fatal train accident in Dublin

Updated 26 December 2018

In 1895 Hamilton’s eldest son, William Edwin, published the second edition of his autobiography annex description of Chatham, Ontario towards the end of the nineteenth century, Peeps at my life. This "pamphlet", as he called it, contains a surprising story, [Peeps 1895, 22]; the very vivid description of the tragic death of Edward James Senior, who was killed by a train on Tuesday the 7th of March 1865, in what must have been one of the early railway accidents in Dublin; the first one apparently happened on the 5th of June 1854. Edward Senior was a Poor Law commissioner, and a younger brother of Nassau William Senior (1790-1864), an English barrister and political economist.

Edward Senior’s death was announced in The Spectator of 11 March 1865: Mr. Edward Senior. The Spectator writes: “Mr. Edward Senior, the brother of Mr. Nassau Senior, so well known for his notes of foreign dialogue and poor-law commissions in Dublin, has followed his brother speedily to the grave. His end was a terrible one, being killed while crossing the Galway railway near Phoenix Park, Dublin, on Tuesday last. He was only 58 years old. It seems that he was in the habit of walking home to his house, Ashtown Lodge, through the park, and of crossing the railway at a level crossing. The policeman on duty frequently remonstrated with him for crossing when a train was in sight, and he wrote to the directors to complain of this annoyance, saying that being warned he accepted the responsibility of passing, and desired not to be worried about it. He was notwithstanding earnestly warned on this occasion, and again accepted a responsibility of which he did not know the extent.”

The ‘earnest warning’ and the ‘extent’ were described by William Edwin in his Peeps: ““Ye maun na gang across,” bawled the dark and sinister-looking High-lander, gateman at the Ashtown level crossing of the Midland Railway, near Dublin, a crossing which combined all conceivable elements of danger, being on a steep grade and a sharp curve, in the concavity of which tall willows were planted to blind the outlook of the engine driver. Senior, relative and namesake of the celebrated Professor and a great Government official, being Secretary to the poor-law Commissioners, was walking home to this country villa. The large gate barred the roadway, but he passed through the turnstile. “D—n it ye maun na pass,” shouted Sandy, roughly collaring him. The roar of the Express shook the willows. The earth trembled. Black clouds of sulphurous smoke heralded the unseen demon. Enraged at his presumption, Senior angrily shook him off, thinking he had time to clear the train, but the delay of two seconds was fatal. Had he been completely let alone or completely held prisoner, he would have been alive to-day. Fragments of hair and bloody bones strewed the track. My father terribly shocked, sent me with a letter of condolence to the widow next morning.”

Nowadays, there is a house called Ashtown Lodge in Castleknock. It is located at River Road, north of Phoenix Park and the crossing, and south of the Observatory and Dunsinea, now Teagasc Ashtown Food Research Centre, where in 1865 the Rathborne family lived. If this was indeed Senior’s house, then the crossing must have been at the contemporary Ashtown station. Virtually standing on the crossing, it can be seen that the tracks are far more curved that they seem to be when seen on a map: Ashtown Crossing, looking towards Dublin. Also at the other side the tracks are curved but further away: Ashtown Crossing, looking away from Dublin, or zoomed in making the sharp curve visible, Ashtown Crossing, looking away from Dublin, zoomed in. It seems possible to notice the train in time from this side though, making it more plausible that the train came from Dublin. Perhaps the situation is not exactly the same anymore; the steepness William Edwin writes about does not show in this link, but such details are generally hard to see in these streetviews.



Utrecht, 7 July 2017 — Summerhill House, Langfords and Longfords, and Hamilton’s account from within the house

In hindsight I should have read through the essay at least one more time, my English having been slightly improved along the way. But alas, I did not. Now working on an extensive corrigendum for the essay, I came across some sources mentioning either Lord Langford or Lord Longford as owner of Summerhill House after the death of Baron Langford in 1825. The once famous house in county Meath was built in 1731 by Hercules Rowley and Frances Upton, and in 1825 their great-granddaughter Frances Rowley and her husband Clotworthy Taylour, Baron and Baroness Langford, still owned Summerhill House. Yet it is not at all clear who owned the house after the Baron’s death, see Summerhill House.

In 1824 and 1825 Hamilton apparently regularly visited the Disneys who, according to Graves, lived in Summerhill House. Hamilton briefly described it from within: once in a letter written to his sister Eliza in September 1825, in which he described how enormous it was, see pp. 57-58 of the essay, and once in 1850, when he mentioned its ‘great decay’, see pp. 297-298. A description of the history and some pictures of the interior of the house can be found at: archiseek – Architecture of Meath & Lost Buildings of Ireland and Summerhill House – The Irish Aesthete.

What Hamilton wrote to Eliza in 1825 was: “I am now, as you will observe by the date, in Summerhill. If you wish to have a more minute description, know that I am in the chamber of the eastern wing upon the north side of the castle, as I conclude from the stars – time midnight, as I learn from the deep tolling of the clock in the tower. A shaded lamp is burning before me; all is quiet now except the audible ticking of my watch; both doors of my room are open, one of which leads to a suite of uninhabited apartments, so long that my light only shows their gloom, through which the beams wander without filling their extent. Hark! what sound is that which comes from their obscurity? it is only the creaking of a door; [...] I am in a castle, with windings and recesses enough to please you and to satisfy even the passion for exploring which we had when children.”



Utrecht, 31 October 2016 — Paper copies, an epub version of ‘A Victorian Marriage’, and ereaders

The essay has been printed, and really does look like a book. It is slightly (much) thicker than I had expected; e-books do not show much volume... . I also made an epub version, with clickable links. Unfortunately, since I did not define page numbers, the in-document referencing is rather imprecise. The epub has been tested in Firefox and on a Kobo Glo: Firefox is not very good at following links to other places within the same document, the Kobo does not show some doubly accented Greek letters. For the rest it seems fine.

Update 1 Sept 2017: My new Icarus Illumina 9.7 inch handles the Greek very well, but to my great surprise it cannot handle internal links: it more or less follows the links, but there seems to be no way to return to the page which contains the link. In Firefox the back button can be used to go back; the Kobo Glo provides a link called ‘Previous location’. It is really very strange that such a function seems to be omitted in a high-quality e-reader, which the Icarus Illumina certainly is (it can be written upon using its stylus, which is great for correction purposes!).



Utrecht, 18 September 2016 — Files sent to the printer, and a search for Hamilton’s birth house

The ‘weeks of editing’ became almost a year but I finally uploaded the final version and sent the files to the printer. I had no idea that editing was so much work, and although the ideas in the essay did not fundamentally change anymore, they did evolve again. Also remarks from people who were so kind to read the drafts almost unvariably led to changes bringing along more changes; luckily, already as a child I was tested as thinking rather lightheartedly about tough jobs.

In 2015 we had come to Dublin very unprepared, and when we became curious where Hamilton’s birth house could have been we could not find it. But the internet is a remarkable thing: not only did I never see Graves’ biography in a paper form although I worked with it for two and a half years, back home we found Hamilton’s birth house after a weekend of searching on the web. Through Hamilton’s own descriptons and a lot of websites with old and new street maps of Dublin, historic information especially about the famous plasterwork (some examples) of No 20, and a description in the Dominick Street Regeneration plan of 2010, it appeared to be, in hindsight, rather obvious that what Hamilton called 36 Great or Old Dominick Street is now 33/38 Lower Dominick Street, Bolton Square, apartments 21-40, left side if seen from the opposite side of the street. This pdf describes our search. Someday going to Dublin again will be much harder than finding information which is more than two hundred years old.

And again in hindsight it appears that, in any case in 1907, there was a “tablet” on the house at 36 Dominick Street marking it as the birth house of Sir William Rowan Hamilton: see p. 294 of Chart, D.A. (1907), The Story of Dublin. London: J.M. Dent & Co.. Hopefully some sign will be added again some day.

Update 23 May 2019: Marvellously, on the 13th of May Peter Gallagher of TCD tweeted a picture of what will have been the tablet (to which he commented, “I’m sure Hamilton would appreciate my caustics” :). Would it not be a good idea to attach it to the wall in Dominick Street again?



Utrecht, 22 October 2015 — Attending the Hamilton Walk in Dublin

Last week we were in Dublin; we came to Ireland to attended the ‘Hamilton Walk’ on the 16th. The Hamilton Walk is a walk from Dunsink Observatory to Broom Bridge in commemoration of Hamilton’s discovery of the Quaternions on the 16th of October 1843: The Hamilton Walk. It was an exciting event indeed; being inside the Observatory and walking along the Royal Canal where Hamilton and his wife walked that day!
We stayed in Dublin at the house of a very nice group of young Brazilian people, and we tried to find Hamilton’s birth house in Dominick-street. We could not find it; the house seems to have been teared down, and there is not a plaque or anything referring to Hamilton. Which is a pity indeed.




Hamilton Walk 2015


Professor A.G. O’Farrell speaking at Broom Bridge during the Hamilton Walk 2015
We are also on this photo; I am the one with the long hair and Eli is standing on my right side.



Dublin, 15 October 2015 — Having finished the essay ‘A Victorian Marriage’, corrections are still needed

Although today I finished the essay, there will be edits in the following weeks since, luckily, people are reading it, and they give very useful comments. The ideas in the essay will not change anymore though; having formed gradually over the last year they were full-grown last summer.
When all comments are implemented satisfactorily, and someday they surely will, I will have this essay printed by the BoekenGilde, in a small edition. For anyone who does not mind to read from a screen this essay can be downloaded as a pdf or an epub, or read in the BookReader, A Victorian Marriage : Sir William Rowan Hamilton.



Utrecht, 2 September 2015 — The 150th anniversary of the death day of Sir William Rowan Hamilton (1805-1865)

Today is the 150th anniversary of the death day of Sir William Rowan Hamilton (1805-1865), the famous mathematician who lived most of his life at Dunsink Observatory in Dublin, Ireland. About his work on mathematics and mathematical physics much is written, and that was positive; no-one doubts or doubted his geniality. Also about his personal life much is written, and that was often not so positive; many people doubt or doubted his ability of handling himself.

Already during his life Hamilton had a very bad reputation, having uncommon habits like working hermit-like on books no-one understood and drinking alcohol when that was not customary anymore. Although it was generally acknowledged that someone on the brink of alcoholism, as he often was claimed to have been, would not be able to work on such extremely high levels as he did, yet somehow his alcoholic image seems to cling to him. In this essay it is shown that he was indeed not an alcoholic.


And having lost his first love, it is often simply assumed that he must have been unhappily married, that his marriage failed from the start, and even that his honeymoon already was a disaster. Hamilton on the contrary, wrote in the days before his marriage about the “layers of love and algebra” and the “attraction of Venus”, which does not sound very disastrous. Indeed, nowhere in his first, and largest, biography it can be read that Hamilton was ever dissatisfied with his choice for her; Hamilton’s main biographer even remarked that “he remained to the end of his life an attached husband, just as Lady Hamilton remained an attached wife, as well as a good woman” and “She had brought calm to his affections; she won the good opinion of his friends; and she became to him the centre round which the pleasures, the duties, and the hopes of home were gathered.” The peace Hamilton found in his marriage is so clear that it actually was the main inducement to write this essay.


In the 1880s Robert Perceval Graves wrote Hamilton’s main biography, consisting of three volumes and more than two-thousand pages, mostly filled with letters Hamilton wrote to friends and family. It can be read online at the Internet Archive, Life of Sir William Rowan Hamilton, volume 1 (1882), volume 2 (1885), and volume 3 (1889). In the many years after its publication this biography was often minutely scrutinized, and some sentences of Graves’ extensive biography seem to have assumed a life of their own; reading those sentences on the web, they can easily be traced in Graves’ biography. Yet in some strange way, as far as I know Graves himself, or the circumstances and social boundaries in which he wrote the biography, is never really scrutinized, and that is what I did in this essay. While doing that it was of course not my intention to ruin Graves’ reputation in order to restore that of Hamilton; yet starting to understand where Graves came from when he wrote it clarified a lot.

Graves having focused mainly on Hamilton’s personal life, in 1980 Thomas Leroy Hankins published Hamilton’s second main biography: Hankins, T.L. (1980), Sir William Rowan Hamilton. Baltimore: The Johns Hopkins University Press. In this biography Hankins completes the picture of Hamilton with the many other sides of his life: his work, his religious, political and social life, and his poetry and metaphysics, being intertwined with his mathematics. Moreover, he fills in the gaps Graves left in his biography since he judged some events to personal for a biography; Graves wrote it deep in the Victorian era, in which many personal events were concealed because of the then prevailing very strict social norms. Hankins published letters and facts worth knowing about Hamilton’s first great love, Catherine Disney, therewith evoking a much more complete picture of who Hamilton was. Yet, since Graves had known the Hamiltons personally, Hankins accepted Graves’ view on Hamilton’s personal life.

The gossip about Hamilton started already during his life, and when Graves had to decide whether or not to accept the task of writing the biography that played a part in his considerations. He described how he accepted the task in the preface to the first volume; “wishing that the memory of my friend had been more fortunate, but at the same time conscious that by me would be devoted to it the warmth of honest affection and admiration, and the desire to be just and truthful.” But not only did Graves find the gossip difficult, he also disapproved of Hamilton’s lifestyle; Graves clearly lived his life very differently from the way Hamilton lived his. What Graves also found very difficult was Hamilton’s choice to marry Helen Bayly; according to Graves everything would have been different if only she could have handled him better and make him live a healthy and ordered life. The apparent impossibility thereof is also described in this essay.

While writing the essay it became clear that there are some loose ends which can only be answered by reading original correspondences. Obvious examples are a letter Hamilton wrote to his friend Lady Campbell in 1830, after he had noticed the unhappiness of Catherine Disney, his ‘lost love’, yet Graves did not want to give this letter since he judged it too personal. The same holds for a letter to Aubrey de Vere which Hamilton wrote in August 1848 when he was in Parsonstown, and a letter to “an unnamed friend” written in 1849; these letters all have to do with Catherine Disney. And it holds for the many letters he wrote after Catherine’s death since in this essay it is suggested that Hamilton only learned about Catherine’s forced marriage on her deathbed, explaining the heavy impact their “parting interviews” had on him.

About Hamilton and drinking alcohol perhaps the most important missing information is what Lady Campbell said, sometime between 1848 and 1851 or 1854, when she warned Hamilton about his drinking habits. Graves does not give an exact quote, he just writes that she “had not failed earnestly to plead with him his own cause, when she heard of the danger that threatened him of being dominated by a fatal habit”, this fatal habit being drinking alcohol regularly, instead of mainly at dinners. Graves’ choice of the words “fatal habit” seems to suggest that Hamilton was already on the brink of becoming an alcoholic, yet reading it carefully, Graves actually writes that Lady Campbell warned Hamilton not to become dominated by a fatal habit, she did not say that he was dominated by this habit already. It is even unclear whether or not she used the word fatal, or whether that was Graves’ interpretation. It is also unclear from Graves’ biography if Graves read this in a letter written by Lady Campbell, or in one of Hamilton’s notebooks or journals in case it was said in a conversation. Her letter, or Hamilton’s note about it if it was a conversation, could very well contain the most clear information about how far Hamilton ever was in developing this “habit”.

[Added November 2017: Also one of Graves’ brothers warned Hamilton, yet that concerned Hamilton’s reputation. Every now and then, after periods of working hard and apparently rather abstemiously, he drank much when he was in public and enjoying himself. The influence of the Temperance Movement was growing, and Hamilton therefore was much gossiped about. Following these warnings Hamilton did not stop drinking alcohol, yet he immediately changed this behaviour; always having been temperate at home he also publicly did not drink much anymore, but by then his reputation in this respect was already ruined. Hamilton became a moderate drinker for about a decade, and it seems that when his gout got worse he stopped drinking alcohol altogether. Hankins wrote, “The physician [who wrote the report on Hamilton’s death], added a statement, that he had called on Hamilton “very unexpectedly early and late ... to watch the progress of his health under such mental pressures and I take leave solemnly to declare that I never found him under the influence of alcoholic stimulants – Moreover I am of the opinion the human mind would be rendered quite incapable of executing such a mighty task if the functions of the human brain were tainted by intemperate habits, to which it has been alleged Sir William was subject.””]

And what would shed some more light on Hamilton’s daily life are letters he wrote to friends and neighbours; Graves mostly gives letters written to members of the peerage or to eminent scientists. But Hamilton must have written many more because it is, for instance, certain that he corresponded with John Head, Dean of Killaloe, who was ‘connected to’ Helen Bayly, yet no letters are given. Missing is also the correspondence between Sir and Lady Hamilton; judging by some letters given by Graves it can be assumed that Hamilton more often wrote letters to his wife when travelling, for instance when visiting the annual meetings of the British Association for the Advancement of Science.