Abstract
This chapter charts Ellis’s mathematical education, from his childhood in Bath under the tutelage of Thomas Stephens Davies to the end of his student days at Cambridge when, in January 1840, he graduated as senior wrangler.
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1 Introduction
Beginning in the spring of 1825 Ellis was tutored in mathematics at home by the upandcoming Thomas Stephens Davies (Fig. 2.1). After Davies’s departure from Bath in 1834 for the Royal Military Academy in Woolwich, Ellis prepared himself for Cambridge without a tutor, apart from a very brief sojourn as a pupil of James Challis. He went up to Cambridge in October 1836, graduating in the coveted position of senior wrangler in January 1840, with four publications already to his name.^{Footnote 1}
Using Ellis’s private journals as a guide, I shall follow Ellis on his mathematical journey from his home in Bath to his triumph at Cambridge. The journals provide a remarkable record of his mathematical education from young boy to mature student. Full of information about the mathematics he was studying—the texts he was reading and the mathematical problems he was trying to solve—as well as his hopes and fears for his own mathematical progress, especially while at Cambridge, they provide a unique insight into the development of one of England’s most gifted mathematicians of the nineteenth century.
When at home in Bath, Ellis had access to a wide range of mathematical texts, many only recently published. Apart from his father’s library, there was the excellent library of the Bath Literary and Scientific Institution (BLSI) to which he was a frequent visitor.^{Footnote 2} He also borrowed books from Davies. It likely that Ellis’s earliest mathematical tuition came from his father, Francis Ellis, who himself had a reputation in Bath as a competent mathematician, and who, on recognising his son’s talents, engaged Davies as a tutor.^{Footnote 3}
2 Thomas Stephens Davies (c.1794–1851)
Davies first appeared in the Ellis household sometime in the spring of 1825 when Ellis was aged only seven,^{Footnote 4} presumably employed on the strength of a personal recommendation. There is no evidence that Davies ever had a fixed position while in Bath; his living seems to have been made solely through tutoring. Certainly by 1830 he was describing himself as a private teacher of mathematics.^{Footnote 5} As well as tutoring Ellis, Davies occasionally gave tuition to Ellis’s older brother Francis (known as Frank). The earliest reference to Davies in Ellis’s journal occurs on 28 May 1827, the day after Ellis began his first journal, where he mentions spending an hour and a quarter with Davies.
Little is known about Davies’s early life. His birthdate is given variously as 1794 and 1795, and it is possible that he came from Wales.^{Footnote 6} By his own admission, he had ‘not a single hour’s of mathematical [Davies’s emphasis] instruction’ and considered himself an ‘nonacademic’ man, but that is all he disclosed about his (lack of) education.^{Footnote 7} His earliest mathematical publications show he was in Sheffield by July 1817 and in Leeds shortly thereafter.^{Footnote 8} He was certainly in Bath by the autumn of 1824 and remained there until 1834.^{Footnote 9} Why he made the move to Bath is unknown but it may be connected to the presence of William Trail who had retired there in c.1821, having been professor of mathematics at Marischal College in Aberdeen (1766–1779) before moving to Ireland for a career in the church. The anonymous writer of a posthumous appreciation of Davies remarked on Davies’s ‘early intimacy’ with Trail.^{Footnote 10} Trail was the author of the popular Elements of Algebra for the Use of Students in Universities (1770), and a biography of the eighteenth century Scottish geometer Robert Simson. Davies was known for his love of classical geometry and this may well have been stimulated by Simson’s edition of Euclid’s Elements, together with Simson’s other writings, the study of which would have been encouraged by Trail.^{Footnote 11}
Once in Bath Davies immersed himself in the intellectual life of the city, becoming an active member of the BLSI of which Francis Ellis was one of the founders. By the early 1830s he was involved in the organisation of the BSLI’s monthly lectures and gave lectures there himself,^{Footnote 12} having gained a scientific reputation cemented by election to national societies. The latter included the Astronomical Society of London in 1830, for which he was proposed by Francis Ellis,^{Footnote 13} the Royal Society of Edinburgh in 1831, and the Royal Society of London in 1833.^{Footnote 14} He attended the second and third British Association for the Advancement of Science meetings which were held in Oxford (1832) and Cambridge (1833), although he did not make any formal contributions. Rather to his surprise, the meeting in Cambridge turned out to be more pleasant than he had anticipated.^{Footnote 15} Contrary to his expectations, he found Peacock ‘delightful’, Airy ‘modest and retiring’, and was even ‘satisfied’ with Whewell.^{Footnote 16}
Alongside his tutoring, Davies continued his geometrical research, publishing in several periodicals including the Philosophical Magazine, the Ladies’ Diary, the Gentleman’s Diary and Leybourn’s Repository.^{Footnote 17} His contributions included answers to mathematical questions as well as articles, usually on an aspect of classical geometry in which he displayed both mathematical expertise and a wide range of historical knowledge. Typical of his publications from this period are ‘Properties of the trapezium’ and the related ‘Properties of Pascal’s hexagramme mystique’ which appeared in the Philosophical Magazine in 1826.^{Footnote 18} Rather more substantial are his publications in the Transactions of the Royal Society of Edinburgh (TRSE), such as those on sundials and on spherical geometry.^{Footnote 19}
One of Davies’s friends while he was in Bath was the Rev. Henry F.C. Logan, professor of mathematics at the Catholic College of Prior Park, with whom he collaborated on problems of spherical geometry.^{Footnote 20} There were plans for a joint publication but in the summer of 1834 they had a fallingout. This was recorded by Ellis in his journal (27 June 1834), although the exact circumstances of the disagreement are hard to fathom. Ellis himself got on very well with Logan and their friendship endured to the end of Ellis’s life.^{Footnote 21}
In the summer of 1834 Davies departed from Bath to take up a post as a mathematical master at the Royal Military Academy at Woolwich where he remained until his death in 1851.^{Footnote 22} While at Woolwich he published extensively in an increasing variety of journals^{Footnote 23} securing his reputation as a geometer.^{Footnote 24} Most of his work was concerned with solving problems arising from classical Greek geometry; one of the exceptions being his geometrical investigations on magnetism about which he corresponded with Mary Somerville.^{Footnote 25} He is best remembered for his Solutions of the Principal Questions of Dr Hutton’s Course in Mathematics (1840), and his subsequent masterful editing of the 12th edition of Hutton’s two volume Course (1841–1843).^{Footnote 26} Less well known is his lecture ‘On the Velocipede’ which he delivered in Oxford in May 1837, a manuscript copy of which survives at Trinity College, Oxford.
Ellis received tutoring from Davies three or four times a week, with Davies’s visits often lasting well over an hour. On the days when Davies was not present, Ellis often worked at mathematics by himself, sometimes on problems Davies had set him to solve and sometimes pursuing his own interests. (This contrasted with his tutoring in classics which took place daily during the week.)
In the early years, Davies and Ellis got on well together, with Ellis keen to ensure he was properly prepared for his next lesson. But as time wore on, Ellis became less tolerant of Davies with his unreliable timekeeping and lack of preparation.^{Footnote 27} Ellis would also run into Davies at the BLSI and although Ellis had broad interests for someone of his age, he had little patience for discussions with Davies on anything other than mathematics; talk of ‘mimosa & geraniums’ had Ellis wishing Davies ‘at the Antipodes’! (23 [22] April 1829). On the personal side, Ellis considered Davies rather boorish with social pretentions.^{Footnote 28} And he had little time for Davies’s wife. He considered her quite unfit for the role and wished he could get Davies a divorce! (8 July 1834).
Whether Davies and Ellis saw each other again after Davies left Bath is unknown but they remained in contact.^{Footnote 29}
3 Ellis’s Mathematical Development (1827–1834)
Ellis’s aptitude for mathematics showed itself very early. Not many children aged nine would have welcomed their father giving them a copy of Legendre’s Elements of Geometry, a book generally considered appropriate for students in higher education (20 June 1827).^{Footnote 30} Ellis relished it. He worked through it with Davies and on his own, at times challenging himself to prove propositions before looking at the given proof. He even took it with him on holiday in Weymouth. Within three months, he had completed the first ‘book’ (chapter) which concludes with the proof that the two diagonals of a parallelogram divide each other into equal parts. Six months later, he had completed the next three books and much more besides, as he revealed in his journal when he listed his achievements of the previous ten months, the period during which he had been writing his first journal. The five at the top of his list (of ten) were mathematical, all of which had made him ‘exceedingly happy’ (28 March 1828)^{Footnote 31}:

1.
I have done quadratics & cubes & begun 2 logs.

2.
I have begun Geometry to 4 books of first Legendre.

3.
I have begun to learn Trigonometry.

4.
I have begun to understand Analysis

5.
In doing Analytical Conic Sections.
He soon moved on to other branches of mathematics, with a variety of textbooks aiding his study. Several were authored by Cambridge graduates and written either for preparation for Cambridge or for use by undergraduates. These included books on conic sections by James Hustler (1820) and Samuel Vince (1817), analytical geometry by Henry Parr Hamilton (1826),^{Footnote 32} mechanics by Bewick Bridge (1813–1814), algebra by John Young (1823) and John Ross (1827), and for logarithms and mathematical tables he was guided by Charles Hutton (1795). Of these, he was particularly taken with Bridge’s Mechanics, extolling both Bridge’s treatment of the subject and the layout of the book.^{Footnote 33} Never before had he understood ‘why a projectile would (but for the atmosphere) describe a parabola’ but now he understood it ‘perfectly’ (29 March 1829). As well as working from English textbooks, he also referred to classic texts such as La Hire’s La Lieux Géométriques (1679), his tuition in French making such texts accessible.^{Footnote 34}
Typical of his journal entries at this period is one made in February 1829 when he recorded a meeting with Davies:
The first problem I attempted [in Ross (1827)], which is the 16^{th} of the “Problems for equations of the higher degrees” turned out to be a biquadratic. We left it therefore, until I shall have learnt the rule & the rationale of equations of the 4^{th} degrees, & proceeded to the next. But from an ambiguity in the enunciation of the problem we made a mistake in the sense of the author, when we perceived it was too late. (27 February 1829)
The book by Ross is an 1827 translation of a popular German algebra text of 1808 by Meier Hirsch,^{Footnote 35} but the examples that go with the text, which Hirsch published in 1811, had been translated earlier by John Wright.^{Footnote 36} It is probable that the two translations had been bound together. The problem referred to by Ellis is the following^{Footnote 37}:
Four persons, A, B, C, D, have each of them a certain number of pounds in their possession, B 1l. more than A, C 1l. more than B, and D 1l. more than C. If we multiply the four sums by one another, and consider the product as so many pounds, we shall obtain 1168 l. more than we should by cubing D’s. How much has each?
Ans. A 5l., B 6l., C 7l., D 8l.
As Ellis noted, the answer requires the solution of a quartic equation—no mean feat for an elevenyear old!
By the middle of March 1830, Ellis had begun studying differential calculus using Dionysius Lardner’s Elementary Treatise (1825). He made rapid progress. Within six weeks he was on to Taylor’s theorem and by the end of May had begun integration. He subsequently moved on to the generation of curves using the first volume of Jephson’s Fluxional Calculus (1826–1830). In the meantime, Davies had also brought him Wright’s Solutions of the Cambridge Problems from 1800 to 1820 (1825), a sure sign that preparation for Cambridge was in hand; and a few weeks later Ellis began a mathematical memoranda book for recording mathematical problems. By the middle of July, he was immersed in Young’s text on the theory of equations which appeared to him the more beautiful the more he saw of it. Nor was he confined to mastering a single subject at a time: one day he was studying mechanics, the next he was proving propositions from Euclid. Davies also asked him to translate texts from the French, such as Lazare Carnot’s Géométrie de Position (1803).
The last months of 1830 saw a flurry of mathematical activity—he had read Cotes’ introduction to Newton’s Principia, was doing a lot of curve sketching and calculus—and Davies was pleased with his progress. 8 December was a typically active day mathematically:
Attempted to find the value of x & y when tan makes 45^{o} with XX’ for the curve ax^{4} − a^{3}y^{2} = y^{′}x – but as y^{3} comes in, it is irreducible. … Mr Davies and I found the tangents &c of a curve who [sic] equa. I forget but whose shape is
& proceeded through two more cases of integration. (8 December 1830)
Sometimes he put his mathematical knowledge to practical use, such as on the day when he drew a specific ellipse ‘to serve as a model for the glass [mirror] to be put up over the sideboard in the dining room’ (7 [8] March 1831). Nor was his mathematics always serious. On a couple of days he was occupied by the weight of eggs:
I was very idly busy in calculating the weight of eggs till breakfast. My datum was the thing Mr P.B. Duncan^{Footnote 38} told me two years ago, that 270,000 eggs weighed 20 tun [sic]. This gives 602669642837 + eggs to the averdupois [sic, avoirdupois] pound, or 49618+ to the troy pound. (13 March 1831)
I finished my calculation about the eggs by finding that the average weight of a hen’s egg is 2^{oz} 8^{dwt} 16^{gr} 7 Troy weight. (16 March 1831)
while on another he did a statistical analysis of the family cats:
Having measured Tom & Dicky I find this table
Tom
Dicky
Nose [toins?]
23^{in}
18^{1/2}
Tail
10^{in}
12^{in}
Stands
10^{in}
12^{in}
Round.beh. Shoul.
17^{in}
15^{in}½
Thus we see that Tom’s carcase [sic] is bigger than Dicky’s but that Dickey [sic] has the advantage in tail and legs. Qu[estion] are not a cat’s tail & stature always nearly equal to each other? The height of the latter being if anything rather less than the length of the tail. Mem measure all the cats you can catch. (29 March 1832)
Early in 1832, at the age of fourteen, Ellis made his first submission to a periodical. Prompted by an ‘unintelligible’ article by a certain Captain Alfred Burton in the United Service Journal on the classical problem of angle trisection,^{Footnote 39} he sent in a response which his father helped him finesse (8–11 February 1832). Burton’s article had been a response to the translation of a purported proof by a Major in the Austrian army which the Journal had carried a few months before. History abounds with misguided angle trisectors, and predictably these two articles drew several critical responses of which the Journal published only a selection. Some of these appeared under pseudonyms but Ellis’s was not among them.^{Footnote 40} Ellis himself expressed dissatisfaction with his paper, at one point wishing it to be ‘at the bottom of the Red Sea’, probably because he was fed up with the subject rather than because his mathematics was flawed. A couple of years later he returned to the subject reading a French tract^{Footnote 41} which he dismissed rather pithily, showing his ability to criticise others and a maturity in his mathematical reading:
Azemar is evidently no mathematician & Garnier’s part is not masterly. The slightest performance of Euler or McLaurin has a finish, an elegance which inferior men never reach. (30 March 1834)
Even if Ellis had felt relieved that his first attempt at publication was unsuccessful, he would surely not have been pleased to discover that a translation of an article he had made for Davies had been published under Davies’s name. In 1835 an article by Davies on spherical trigonometry appeared in Leybourn’s Mathematical Repository. It was dated 25 October 1832 and contained a result which had appeared in Latin in 1825 in an article by the German mathematician Carl Jacobi, and Davies had promised to produce a translation of this article for a future issue.^{Footnote 42} Three weeks later, Ellis reported in his journal that Davies had asked him to translate Jacobi’s article, a request to which he had acceded with reluctance and later regretted (12 November 1832, 3–4 February 1833, 12 May 1833). Presumably Davies had found the translation more difficult than he had anticipated. When the translation—which took Ellis several months to complete and ran to 30 pages—was eventually published, it appeared as if produced by Davies with no mention of Ellis.^{Footnote 43} By this time Davies was safely in Woolwich!
Given Davies’s own interests, it is not surprising to find that much of Ellis’s time with Davies was spent studying geometry. Euclid’s Elements was a constant of young men’s education in the nineteenth century, and Ellis was no exception. But the Elements was not a text Ellis universally relished. In the summer of 1832, he was very relieved to have finished the first two Books (which deal with the properties of plane figures made from straight lines) after four years of acquaintance. He was much happier once he had moved on to Book 3 and the theory of circles. He then began the study of solid, i.e. threedimensional, geometry, beginning with the treatise of Hymers (1830) rather than with Euclid, before progressing to Monge’s Géométrie descriptive (1799) in which methods are developed for representing threedimensional objects in two dimensions. It was not a subject he took to, finding it ‘very difficult to conceive’ and hard to remember (17 October 1833). Davies had made models to go with Monge’s text and although Ellis tried his hand at constructing some of his own, he met with little success. He could see the value in constructing them but felt that ‘mechanical matters’, as he described them, were not one of his strengths (21 October 1833), although he had had more success a few months earlier when he had made a model of bees’ cells (24 March 1833).^{Footnote 44} Other geometrical topics he studied with Davies included porisms—a particular favourite of Davies’s—and Legendre on the theory of parallels.
Alongside mathematics, Ellis was exposed to some physics, both with Davies—they studied Whewell’s Dynamics and Mechanics together—and at the BLSI where he witnessed experiments, such as those on hydrostatics by the peripatetic lecturer Robert Addams.^{Footnote 45} He also did various physics experiments himself, sometimes with the help of his father who himself enjoyed experimenting.^{Footnote 46} Initially Ellis struggled with the number of different notions involved (time, space, force, moving force, etc.) but once he could use the calculus he found it much easier. During a trip to London in the summer of 1832 he visited mathematical instrument makers and the newly opened National Gallery of Practical Science. At the latter he ‘saw a spark from the magnet’ which he presciently considered to be ‘the most important perhaps of any electrical discovery since the days of Franklin’ (16 July 1832).^{Footnote 47} What he had seen was an example of Faraday’s famous magnetic spark apparatus which the previous year had caused a great stir at the Royal Institution and which lay at the foundation of Faraday’s groundbreaking work on electromagnetic induction.^{Footnote 48} On the same trip, he read Babbage’s newly published book on manufacturing from which he learnt about Babbage’s difference engine,^{Footnote 49} a small working model of which Babbage had produced earlier that year.
Much of the final year of Ellis’s tuition with Davies, from the summer of 1833 to the summer of 1834, was taken up with preparation for Cambridge in the form of past examination papers—even though Ellis’s planned departure for Cambridge was not until the autumn of 1835—and, especially, the study of Peacock’s Algebra (1830). The latter was the first of Peacock’s contributions to the reform of algebra in Britain.^{Footnote 50} It was particularly notable for Peacock’s idea to distinguish between arithmetical and symbolical algebra, the distinction which led to his celebrated ‘principle of the permanency of equivalent forms’ (Fig. 2.2), as well as for his effort to end the longstanding controversy over the validity of the use of negative and complex numbers.^{Footnote 51} Although, like many of the other texts Ellis had been studying, it was aimed at undergraduates, its innovatory nature and its length of almost 700 pages, made it much more challenging. Ellis concentrated much of his effort on the lengthy third chapter which, as Peacock described in the Preface:
[…] contains a very lengthy exposition of the principles of Algebra in their most general form, of their connection with Arithmetic and arithmetical Algebra, of some of the most important general principles of mathematical reasoning to which they lead, and most particularly of the principles of interpretation of algebraical signs and operations […].^{Footnote 52}
which he read several times.
The following selection of Ellis’s many comments on the text provide an insight into the development of his mathematical thinking as well as documenting his progress:
30 July 1833
Read Peacock’s Algebra ch. 3. It is the toughest sort of book I ever met with. The style is not clear & the views themselves may be, for of this I cannot fairly judge, a little cloudy.
26 August 1833
Read Peacock’s algebra for an hour and a half, and nearly finished the third chapter. The whole of his views are so recondite and abstruse that if they are adopted, we should be obliged to have two systems of algebra, exoteric and esoteric.
26 October 1833
Read Peacock. The ‘principle of the permanency of equivalent forms’ requires as the author says ‘a great and painful effort of the mind’. Very few of those who study Algebra will I think take the trouble of mastering it.
14 April 1834
Read the third chapter of Peacock’s Algebra with Mr Davies. This celebrated third chapter will take us some to study: I mean, to analyse it.
24 April 1834
Read … the twelvth [sic] chapter of Peacock [General Theory of Simple Roots, with the Principles of the Application of Algebra to Geometry] with Mr Davies. The objections which the latter makes to the double use of \( \sqrt{1} \) , being as it were both affection and quantity, seem to me more valid than the majority of his remarks.
5 June 1834
I think that the geometrical part of the twelfth chapter is almost if not without exception the most interesting part of the book. There is a fairness and ingenuity in it which is very unlike the special pleading of some writers on these subjects who seem to have a cause to support, and not the cause of truth, who though not enthusiasts are perhaps fanatics.
19 [21] June 1834
[W]rote some of the analysis of [t]he twelfth chapter. Mr Davies ar[ri]ved today, and we read the [11^{th}] chap. of Peacock on Ratio and proportion. It is the best thing on the subject I know, and is one of the best chapter[s] in the Algebra, both as being very clear, and very ingenious and accurate.
As well as wanting to study the Algebra for its own sake, there was another reason why Ellis would have been keen to be familiar with it. Its author, Peacock, who was then the mathematics tutor for Trinity College, would be the person initially to oversee his mathematical education when he went up to Cambridge. On 9 June 1833 Ellis had received a longawaited letter from Peacock providing him with a course of preparatory mathematical reading. In his letter, Peacock also recommended that Ellis spent the academic year 1834–35 with a private tutor. A year later, Ellis received confirmation from Peacock that he had been entered for Trinity. Following this, he spent the next couple of months in an intensive study of calculus, working through the translation of Lacroix’s Traité Élémentaire du Calcul Différentiel et du Calcul Intégral (1802),^{Footnote 53} as recommended by Peacock and to which he had already been introduced by Davies, and working on Peacock’s Examples (1824). In the meantime, in response to Peacock’s advice, it had been arranged that in October 1834 he would go for tutoring with James Challis, future Plumian Professor of Astronomy and Experimental Philosophy who was then Rector of a village outside Cambridge,^{Footnote 54} in preparation for which Ellis had been sent an extensive reading list.^{Footnote 55}
As Ellis’s time with Davies drew to a close, he reflected on his progress with him. The verdict was not altogether favourable:
I must say that Mr. Davies has sometimes dragged me forward, & at other times for want of a plan has kept me in the same place, so that my knowledge in mathematics is very different from what it might have been. (13 May 1834)
Two months later, just as Davies was leaving, Ellis hardened his views further:
Mr Davies did not come, indeed I no longer expect him – So I read Lacroix by myself – I am determined – if as perhaps I may have, should life and health be spared to me, I ever influence any one’s mathematical education – there shall be no teaching – no jockeying, getting on of the pupil. He shall be left to himself, after the first rudiments – Had this been my case, I had now been a mathematician – for I have fair abilities. (21 July 1834)
His patience with Davies, who had been spending more and more time away, had run its course, and his exasperation with him was palpable. Even so, his assessment seems rather harsh given the extent to which he had developed mathematically during their long association. But Ellis had now surpassed Davies mathematically and there was little more Davies could teach him. Moreover, his preference was for calculus and algebra, and the more abstract the better. There was little room for the geometry of Euclid and the other classical authors so beloved by Davies.
On 24 October 1834, Ellis and his father arrived at Papworth Everard, the village some 13 miles outside Cambridge where Challis was Rector:
We stopped  & got out  & a fussy little man introduced himself as Mr Challis  & two, to my eyes, yahoos as his pupils– However we walked all five about half a mile to his house which is pleasantly situated– & I underwent an introduction to madame, & in an hour I was alone. … We dined at five & began to brighten up – Crowfoot & Barrett are the two beside myself – both gentlemanly.^{Footnote 56} (24 October 1834)
Ellis’s initial reaction to his fellow pupils was hardly favourable– “yahoos” then as now is not exactly a term of endearment. But this occasion would have been one of his first opportunities to see students of his own age with Cambridge aspirations and presumably he expected them to exhibit a similar demeanour to himself.
As far as mathematics was concerned, Challis’ teaching plan was to ‘begin at the beginning’, a plan which Ellis thought not altogether bad, despite the fact that his mathematical preparation was far ahead of that required (25 October 1834). Nevertheless, shortly after arrival he was somewhat surprised to find himself having to study Bonnycastle’s Arithmetic, an elementary textbook, first published in 1780 and designed for use in schools.
Despite plans to the contrary, Ellis’s stay with Challis lasted only six weeks, the ill health which had dogged him throughout his childhood forced an early return to Bath.^{Footnote 57} Although Ellis was due to go up to Cambridge in 1835, his continuing poor health prevented it and resulted in two years of selfstudy before his arrival at Trinity in October 1836. Few of Ellis’s journals have survived from this period, so little is known about his study at this time. However, in the summer of 1835, Ellis did express regret at not being able to return to Papworth Everard. By then he was not only missing the mathematical stimulus from Challis and from being in the company of other students, he also wanted to be away from Bath.
During the spring of 1836, Ellis made many visits to the BLSI to take advantage of the library. He spent much of his time immersed in Lacroix’s textbook on the differential and integral calculus. It was a book he liked, and he read it several times. Some of the other works he studied were more advanced in nature, such as Babbage’s ‘profound essay’ on the calculus of functions (1815–16) which required a ‘great “concentration” of mind’, and Fourier’s theory of heat (1822), neither of which were standard fare for undergraduates let alone for schoolboys (9–10 April 1836; 9 May 1836). He was also in touch with Davies, who sent him copies of his papers on magnetism (Davies 1835b, 1836) which he read attentively.
Although Ellis worked hard to prepare himself for Cambridge, he was not enthusiastic at the prospect of going up, in fact quite the reverse: he became ‘sick of the very name of Cambridge’ (24 May 1836). The highly intensive system of study for the purpose of succeeding in an examination was not suited to his temperament (or indeed for his health) and although he felt he would be unable to do himself justice, he could see no alternative. As the start of term approached, he became increasingly melancholic:
It is useless for me to go to Cambridge. I am not covetous of honours certainly not of university honours. At Cambridge I shall only waste the best years of what will probably not be a long life, in regrets bitter and unavailing, in ceaseless mortification of spirit, in weariness of the flesh. So easily and so commonly do we lose sight of the end in the means. (1 August 1836)
But, despite such misgivings, to Cambridge he went.
4 Cambridge, 1836–1840
At the beginning of the nineteenth century, the normal route to a Bachelor of Arts degree at Cambridge was through the SenateHouse Examination, popularly known as the Tripos. The examination was primarily in mathematics but included other subjects, such as logic, philosophy and theology. It began to be referred to as the Mathematical Tripos only in 1824, when the Classical Tripos was examined for the first time, although students could enter the Classical Tripos only if they had already obtained honours in the Mathematical Tripos.^{Footnote 58} As the century progressed the examination took on an everincreasing significance. There was a shift from oral to written examinations, with success in the final examination being paramount, and a concomitant rise in private tutoring without which such success was virtually impossible. It was a fiercely competitive examination and a high place in the order of merit—to be a wrangler or more especially senior wrangler—garnered national recognition and was a passport to the career of the graduate’s choice.^{Footnote 59}
Mathematics was the core of study at Cambridge not because it was preparation for a career as a mathematician but because it provided a fundamental part of a liberal education, the notion so strongly advocated by William Whewell.^{Footnote 60} The reason for studying Euclid’s Elements was not simply to learn geometry. It was a training of the mind. That said, knowledge of Euclid provided (at least some) access to the single most important text a Cambridge mathematics student had to study: Isaac Newton’s notoriously difficult Principia. Written primarily in the language of geometry, the Principia provided the most certain demonstration of human knowledge of the natural world. Mathematics also had the advantage that it provided a level playingfield in the final assessment of undergraduates, or at least that was the thinking at the time.
4.1 Tuition
When undergraduates began their mathematical studies, they did so under the direction of the college mathematical lecturer whose duties were to guide their reading and prepare them for the rigours of the college and the SenateHouse examinations. When Ellis arrived at Trinity, Peacock was both the mathematics lecturer and a college tutor, so it was to Peacock he was expected to turn when he required guidance. But Ellis, who had already mastered much undergraduate mathematics and was far more advanced mathematically than his peers, had little need of such guidance. His contemporary Harvey Goodwin recounts how Ellis was ‘much amused’ by Peacock’s surprise on discovering that Ellis, soon after arrival, was reading Robert Woodhouse’s 1810 historical treatise on the calculus of variations,^{Footnote 61} a publication aimed at a mature mathematical audience and certainly not written with students in mind.^{Footnote 62} As well as the tuition provided by the college, there were lectures delivered by the professors. Not all students attended the lectures of the mathematics professors, and not all the mathematics professors lectured. While Ellis was an undergraduate the Lucasian professors—Charles Babbage, who held the chair from 1828 to 1839, and Joshua King, who held the chair from 1839 to 1849—never lectured. Peacock, who had been appointed to the Lowndean chair in 1837, lectured on astronomy and geometry, and Challis lectured on hydrodynamics, pneumatics, and optics, giving practical demonstrations.^{Footnote 63} Ellis attended these lectures but never took notes or asked questions. As he told Goodwin, the only reason he went to the lectures was to avoid the trouble of having to read up the subjects for himself.^{Footnote 64} Challis’ experiments, such as those with airpumps, did not excite him either.
George Peacock’s Lowndean Lectures
‘These Lectures are given in the Lent Term, and the object proposed by them, is to make students acquainted with the present state of the science of Astronomy, and with the practical methods of observation, which are commonly followed in modern Observatories; the most important astronomical instruments or models of them are exhibited, and the use of them explained, either in the Lecture Room, or at the Observatory. As this Professorship was designed by the Founder to comprehend Geometry as well as Astronomy, it is hereafter intended by the present Professor, to give Lectures alternately on Astronomy, and on Geometry, and the general principles of Mathematical Reasoning’ (Cambridge University Calendar (1839), 116).
Another reason for Ellis’s behaviour in lectures, was his delicate eyesight which he protected whenever possible. Not only did he listen to lectures without writing but he often employed someone to read mathematics to him, even technically advanced subjects such as the theory of the figure of the earth as given in Pratt’s Mechanical Philosophy (1836), a text full of complex expressions and equations.^{Footnote 65} That as an undergraduate he could comprehend such mathematics without seeing it written down on the page is quite remarkable.
As well as Euclid’s Elements and Newton’s Principia, there were several mathematical textbooks which Cambridge students were expected to study, many of which had been written by former wranglers and were designed specifically for students of the university. As described above, Ellis was already familiar with many of these, including those of John Hymers who was among the most prolific and influential of textbook writers of the period. Hymers, who successfully combined his college career with private tutoring, had a reputation for being ‘profoundly versed in mathematics’ with a ‘vast acquaintance with the mathematics of the Continent’.^{Footnote 66} The second edition of his Integral Calculus (1835) introduced English students to the newly discovered topic of elliptic functions, while his Treatise on Conic Sections and the Application of Algebra to Geometry (1837) became the standard textbook on analytic geometry. But Ellis was not so easily impressed. He had read Hymer’s analytic geometry with Davies and considered it to be ‘the most ugly amongst books’ (14 November 1832). And Ellis was not the only one to express dissatisfaction with Hymers. It seems Hymers’ capacity for producing textbooks had been somewhat bolstered by the unacknowledged use of the work of others!^{Footnote 67}
The 1816 translation of Lacroix’s introductory textbook on the differential and integral calculus by Babbage, Herschel and Peacock—the book Ellis had studied on Peacock’s recommendation—was an important stimulus for the introduction of analytical methods into Cambridge. It was followed by several new books which treated their subjects from an analytical perspective and became standard undergraduate fare. Among these were Whewell’s books on mechanics and dynamics which Ellis had begun studying at the age of fourteen. Another staple text was George Biddell Airy’s Mathematical Tracts which provided an analytical approach to problems of physical astronomy, the shape of the Earth, and to its precession and nutation, although Ellis considered Airy’s discussion on precession to be ‘very badly done’ (12 July 1839). Originally published in 1826 while Airy was Lucasian professor, the second edition of 1831, which would have been studied by Ellis, included a new section on the wave theory of light. Another book promoted to Cambridge students by Whewell and Peacock, and which Ellis may have read at Cambridge is Mary Somerville’s Mechanism of the Heavens (1831), Somerville’s interpretation of Laplace’s Mécanique céleste.^{Footnote 68}
In his first and second years, Ellis was in the first class in the college examinations, or a ‘Prizeman’ in college parlance, results which he achieved without the aid of additional tutoring. In his allimportant third year and final (tenth) term he was privately tutored by the famous mathematical coach William Hopkins.
4.2 Coaching
Hopkins, who had been seventh wrangler in 1822, was the first of the Cambridge coaches to make a permanent living from private tutoring.^{Footnote 69} He rapidly developed a reputation as an outstanding teacher and his results were remarkable. Between 1828 and 1849, he ‘personally trained almost 50% of the top ten wranglers, 67% of the top three, and 77% of senior wranglers’, which amounted to 108 in the top ten, 44 in the first three, and 17 senior wranglers, and earned him the sobriquet ‘senior wrangler maker’.^{Footnote 70} As Hopkins’s reputation grew, he was able to pick and choose his students. By taking students in their second, or very occasionally, as was the case with Ellis, in their third year, he had time to assess their abilities and select the most promising before taking them into his tutelage. He taught in small classes, putting students of equal ability together which ‘meant that the class could move ahead at the fastest possible pace, the students learning from and competing against each other’.^{Footnote 71} Or as one of his obituarists wrote^{Footnote 72}:
The secret of his success as a teacher was the happy faculty he had of drawing out the thoughts of his pupils and make them instruct each other, while he took care that the subjects under discussion were treated in a philosophical manner so that mere preparation for the senatehouse examination was subordinate to sound scientific training.
Although group coaching with Hopkins was the norm, Ellis appears to have had individual instruction. Unlike his contemporaries, he did not need coaching in mathematics per se, rather he needed his reading to be ‘arranged and put in a form suitable for the Cambridge examinations’.^{Footnote 73} In other words, he needed coaching in examination technique. Although he detested the Cambridge system which he described as ‘the crushing down of the mind and body for a worthless end’ (3 December 1838), he knew if he was to have any chance of being a high wrangler he had to go to Hopkins.^{Footnote 74} And it was no minor commitment. Judging by the fees he paid—£42 for a year’s worth of coaching—he was being coached six days a week.^{Footnote 75} It did not take Hopkins long to ascertain the potential of his student and before the Michaelmas term of 1838 was out he had told Ellis that he expected him to be senior wrangler.
Ellis provided no description of the mathematics he studied with Hopkins, but with his mathematical maturity he probably had more of a say in which subjects were covered than Hopkins’s usual students. George Gabriel Stokes, who was in the year behind Ellis, kept the notes he made while with Hopkins and these give a good idea of Hopkins’s usual style of teaching: theory given, examples worked through, and others left for the student to complete.^{Footnote 76} None of Hopkins’s own notes appear to have survived, although he did publish an elementary textbook on trigonometry in which he used history of mathematics both to elucidate and to motivate the mathematics discussed.^{Footnote 77} Possibly he illuminated his teaching similarly, especially with a student like Ellis who had such broad interests. Although when Ellis read Hopkins’s book back in 1834 he was less than enthusiastic about it:
Finished Hopkins’s trigonometry. It is but a poor thing. Plane trigonometry is to me what the air pump and the electrical machine are to Sir G. Gibbes^{Footnote 78} – a subject of which I am sick. (23 August 1834)
As well as tutoring Ellis, Hopkins also included him in social events. Sometimes these were dancing parties at which Mrs. Hopkins would provide partners for the young men ‘according to their university reputation’ (30 November 1839). Naturally Ellis was high on Mrs. Hopkins’s list and on one such occasion he found himself in the happy position of dancing with ‘the great Cambridge belle’ Miss Lorraine Skrine, as well as with ‘two other stars of less magnitude’.^{Footnote 79} He spent another evening in the company of three senior wranglers—Challis, Philip Kelland and Archibald Smith—together with George Green and Duncan Gregory.^{Footnote 80} Hopkins also maintained contact with Ellis out of term. When Ellis was staying in Dover during the summer vacation, Hopkins suggested to him they might meet for the day Boulogne. Ellis kindly declined.
Many years later, Hopkins related his memories of Ellis as a pupil:
On one point he always seemed to puzzle me. The extent and definiteness of his acquirement, and the maturity of his thought, were so great, so entirely pertaining to the man, that I could hardly conceive when he could have been a boy.^{Footnote 81}
Clearly Hopkins saw Ellis as exceptional and someone to be treated exceptionally. It is probably fair to say that their relationship was more like one between two colleagues than one between a master and his pupil.
5 Examinations
At the beginning of 1839, Ellis’s return to Cambridge was delayed several weeks by an attack of measles. When he did return, it was with a heavy heart. He felt sick of Cambridge and the whole wranglermaking process and yet he had almost another whole year ahead of him.^{Footnote 82} But he had already invested so much in the system that, despite his misgivings and doubts of success, there was nothing for it but to continue. He came top in the college examinations that summer, as he had anticipated, but even that gave him little comfort. And as Hopkins and Peacock continued to reiterate their belief that he would be senior wrangler, and so he continued to be full of selfdoubt. The Michaelmas term brought further college examinations as well as examinations with Hopkins, and study for the looming Tripos intensified.
The term ended and he, together with several fellow students, remained in Cambridge for Christmas and New Year, preparing for the Tripos examination which started on 6 January.
There were six days of examination, with the papers becoming progressively more difficult.^{Footnote 83} The questions were of two types: bookwork and problems. The former required students to reproduce standard definitions, theorems, and proofs, while the latter tested students’ ability to apply what they had learnt to increasingly technical and challenging problems. These were not problems to be found in the back of books but problems constructed specifically for the examination, and it was not unusual for the examiners to base questions on their own research. Importantly, it was the problems that effectively determined the order of merit. There were two papers each day, twoandahalf hours in the morning and three hours in the afternoon, making a total of thirtythree hours examination altogether. The papers were set by two Moderators and two Examiners who undertook essentially the same tasks, the only difference being that the Moderators were responsible for the ‘papers of original problems’, i.e. for the more difficult ones.^{Footnote 84} In 1840, the Moderators were Alexander Thurtell (4W 1829) and Thomas Gaskin (2W 1831), and the Examiners were Henry Wilkinson Cookson (7W 1832) and Archibald Smith (SW 1836), none of whom made a career in mathematics.^{Footnote 85} Every undergraduate had to take the first four papers and a failure to pass resulted in the student being ‘plucked’; i.e. not allowed to continue his studies.^{Footnote 86}
For those aiming for high honours, preparation for the Tripos was a punishing experience; it is little wonder that the health of students was sometimes compromised, and their performance affected. It was a regime under which Ellis with his poor health could well have buckled. But as the American Charles Bristed, who studied for the Tripos between 1841 and 1844, described, Ellis was the exception that proved the rule:
Indeed a man must be healthy as well as strong—“in condition” altogether to stand the work. For in the eight hours aday which form the ordinary amount of a reading man’s study, he gets through as much work as a German does in twelve; and nothing that our students go through can compare with the fatigue of a Cambridge examination. If a man’s health is seriously affected he gives up honors at once, unless he be a genius like my friend E[llis], who “can’t help being first”.^{Footnote 87}
The examination itself produced its own casualties. In 1842 the second wrangler, C.T. Simpson, ‘almost broke down from over exertion […] and found himself actually obliged to carry a supply of ether and other stimulants into the examination in case of accidents’.^{Footnote 88} Worse was to happen in 1843 when ‘a singular case of funk occurred’ and the candidate concerned, T.M. Goodeve, ran away after four of the six days of examination and was found outside Cambridge some time afterwards.^{Footnote 89} Goodeve had been expected to be second wrangler but ended up as ninth, his absence thus proving not too calamitous. Indeed, as Bristed observed, the papers of the final two days affected the places of only the best ten to fifteen students.
When it came to Ellis’s turn, there were 171 questions to be tackled over the course of the twelve papers (Fig. 2.3). Candidates were eased in on the first day with two papers being mostly bookwork, one in mathematics and one in natural philosophy, with explicit instructions not to use the calculus. These included standard questions requiring the reproduction of proofs from Euclid’s Elements and knowledge of the first book of Newton’s Principia. The next three days each included a problem paper and the rest of the papers were equally balanced between mathematics and natural philosophy. The majority of other questions were on algebra, the calculus, mechanics, dynamics, astronomy, hydrostatics and optics, with a few on heat, electricity and magnetism.
Many of the questions in the natural philosophy papers were clearly contrived, although some had a semblance of applicability about them. Notable among the questions of 1840 was one about a train on an inclined railroad, probably the first time that the railway had featured in the examination. (Cambridge would not have a railway station for another five years.) The artificial nature of the problems was wellknown and contributed to ongoing debates about the content of the examination and fuelled calls for reform. In 1841 Peacock made his views on the subject clear:
The problems which are proposed in the senate house are very generally of too high an order of difficulty, and are not such as naturally present themselves as direct exemplifications of principles and methods, and require for their solution a peculiar tact and skill, which the best instructed and most accomplished student will not always be able to bring up on them. It is not unusual to see a paper proposed for solution in the space of three hours, which the best mathematician in Europe would hesitate to complete in a day.^{Footnote 90}
Lurking amongst the 171 questions was one that related directly to Ellis’s later research. It was posed as the final question on the fourth day of papers and began by asking for an explanation of the nature and use of the method of least squares. Five years later, Ellis would write a paper on exactly this topic, showing himself to be one of the few people at the time who understood Gauss’s contribution to its development.^{Footnote 91}
Ellis had one possible rival in the examination, Harvey Goodwin, who was also coached by Hopkins. Speculation was rife that Ellis’s health might not stand up to the intensity of the examination which would give Goodwin his chance. But Goodwin acknowledged Ellis’s mathematical superiority and recognised that should such a victory over Ellis occur, it would be a hollow one:
Few things could have been less satisfactory than to find oneself decorated with a false halo of glory in consequence of the physical weakness of an incomparably superior man.^{Footnote 92}
Cambridge in early January can be a bitter place, and previous years had brought sufficient complaints about the coldness of the Senate House, that, as a temporary measure, the examination had been moved to Trinity. Candidates sat at long tables and the original seating arrangement, which students could inspect beforehand, had Goodwin and Ellis sitting almost opposite one another. For an unknown reason, possibly related to his health, Ellis asked to be moved to a different room, whether to be on his own or not, is unclear.^{Footnote 93} Aside from venting dislike of the problem papers on the third and fourth days, Ellis wrote almost nothing in his journal about the examination, although he did describe his social activities, such as playing backgammon with his college friends.
The results came out on 14th January, the day after the final paper, and, as was common practice, they were widely circulated in both the national and local press. As predicted by all who knew him, Ellis was senior wrangler. Smith told him that it was not even close, and that he was ahead of Goodwin, who came second, by more than 300 marks.^{Footnote 94} He had even ‘beaten’ a paper, that is he had been awarded more than full marks for it; the extra marks being given for style in the bookwork.^{Footnote 95} Hopkins described Ellis as ‘a senior wrangler among senior wranglers’ (14 January 1840), and Peacock’s reaction was to tell Ellis that he ought to get a fellowship at the first attempt which made Ellis think it worth a try.^{Footnote 96} Later in the day, he celebrated by drinking sauternes with his fellow examinees Alexander Gooden and Richard Mate.^{Footnote 97}
The ceremony at the Senate House at which degrees were conferred took place the following day. Ellis was a popular success, and great cheering rang out when he was presented to the ViceChancellor.^{Footnote 98} It was a theatrical occasion and, as he described in his journal, he was looked after by his friend, Joseph Hume (26W)^{Footnote 99}:
At ten to the Senate House. Put on bands and hood, Hume sedulously superintending. Then mingled in the crowd: congratulated and was congratulated. Mrs Challis sent for me, & I went & spoke to her. Whewell came up & after congratulations hinted at the impropriety of being where I was; for which I relief I felt obliged. I returned to the bar where my friends were. Hopkins sent me down to the platform as I was to be marked up all the way. When all was ready, he and the other esquire [B]edell^{Footnote 100} made a lane with their maces, and Burcham led me up. Instantly, my good friends of Trinity & elsewhere, two or three hundred men, began cheering most vehemently, and I reached the Vice [Chancellor]‘s chair surrounded by waving handkerchiefs & most head rending shouts. Burcham nervous; I felt his hand tremble as he pronounced the customary words “vobis praesento hunc iuvenem”. Then I took the oaths of allegiance and supremacy and knelt before the Vice [Chancellor], who pattered over the “Auctoritate mihi &c” and shaking hands wished me joy. I turned back, & walked slowly & stiffly down the Senate House. More cheering. Hume met me, & led me to the open space just at the bottom – made me sit down, & said I was pale. – which I suppose was true, as I did not feel the excitement the less for showing but little symptom of it. Up came some gyp, with a bottle of salts, which I declined at first, but was bound in gallantry to take when I found a young woman had sent it to me from the crowd. (15 January 1840)
Goodwin also provided an account of the occasion although his was composed several years later. He recalled Ellis looking exactly the part and remembered his father saying to him that had he caught a glimpse of Ellis earlier he would have told him (i.e. Goodwin) that Ellis was unbeatable.^{Footnote 101} Whatever Ellis might have been feeling inside, it seems he carried the day with composure. But a further trial was yet to come.
The following week the leading wranglers knuckled down again to compete for the Smith’s Prizes.^{Footnote 102} This took the form of more examination papers, each one of which was sat over the course of a day and set by a different examiner. Unlike the Tripos, the questions were mostly geared towards evincing an original or creative approach and often they had a discursive element. Usually only the most distinguished wranglers sat the examination, so the numbers entering were small, and it was not unknown for the number of candidates to be the same as the number of prizes. The prize was worth £25 but its real value was in the academic prestige attached to winning. The competition was a much sterner test than the Tripos and although to the outside world a prizeman did not carry the cachet of a senior wrangler, within the confines of the Cambridge mathematical community the honour was recognized as the ultimate achievement.
In 1840 the examiners were the three mathematics professors, Peacock, Challis, and King, together with the professor of mineralogy, William Miller.^{Footnote 103} Each paper consisted of about 25 questions, from aspects of pure mathematics to the construction and use of scientific instruments, and even the description of experiments. As expected, Ellis once again won the day. Goodwin had a rather harder time winning the second prize. He and Joseph Woolley, the third wrangler, were so close, they had to sit two deciding papers the following week.^{Footnote 104}
Ellis left Cambridge for London on the day the winners of the Smith’s Prizes were announced, his student days behind him. A few years earlier he had thought that a senior wrangler could look to be either Lord Chancellor or Archbishop of Canterbury but no longer.^{Footnote 105} The punishing system had taken its toll and he left with his ambition stifled. He felt ‘like some sick brute who would fain leave the herd to go into a corner and die’ (29 February 1840). Studying for the Tripos and the attendant accumulation of examinations for over three years had put his health under a tremendous strain, both physically and mentally. Moreover, he had not restricted his mathematical output to examinations. During his final year as an undergraduate, he had had four papers published in the Cambridge Mathematical Journal.^{Footnote 106} And he was not only producing new results, he was actively taking issue with old ones, and robustly at that. In his first publication, which concerned properties of the parabola, he referred to a proof by the mathematician and Fellow of the Royal Society, John Lubbock, as ‘tedious’ and proceeded to provide a more elegant one, one which Lubbock did not immediately understand! Ellis made passing reference to Davies in this paper; it was the only time he mentioned him in his work.^{Footnote 107}
In view of what he had achieved, it is not surprising that in the immediate aftermath of the examinations, Ellis felt he had little left to give. But gradually he recovered his spirits and in October, as Peacock had predicted, he was elected to a fellowship at Trinity, and a new phase in his life began. His mode of preparation for the Tripos had been quite different to that of his fellow wouldbe wranglers, and the experience did little to dictate the course of his subsequent career. As one of his obituarists put it, his mathematical interests were ‘as far as possible from being confined to the limits of a Cambridge course of reading for honours’ as they could possibly be.^{Footnote 108}
Notes
 1.
Wranglers were students who obtained firstclass honours in the Mathematical Tripos. They were listed in order of merit with the senior wrangler (SW) being the top student of the year. Henceforth, wranglers will be denoted (XW) where X stands for position, i.e. second wrangler will be denoted (2W).
 2.
For Ellis’s early intellectual life, see Stray’s chapter in the present volume.
 3.
On general aspects of Ellis’s home education, see Stray’s chapter in the present volume.
 4.
On 30 June 1834, Ellis noted in his journal that Davies had been teaching him for more than nine years.
 5.
On 25 May 1830, when he was elected to the Astronomical Society of London (from 1831 the Royal Astronomical Society), Davies, underneath his signature, described himself as a private teacher of mathematics. He also advertised for pupils: The Bath Chronical and Weekly Gazette for 30 December 1830 carried a prominently placed advertisement for Davies as a mathematical tutor, especially for ‘those intended for the Universities, and the Royal Military and Naval Colleges’.
 6.
The grounds for thinking Davies may have come from Wales are that his surname is of Welsh origin and Ellis, punning on Davies’s open dislike of Cambridge, saying that he thought Davies preferred ‘Cambrian mathematics’ to Cambridge (10 June 1833). Davies’s antipathy towards Cambridge would be dispelled after his visit there for the British Association for the Advancement of Science meeting later in 1833 (see below).
 7.
Thomas S. Davies. “University and nonuniversity mathematicians,” Mechanics’ Magazine 46 (1847), 428–431, on p. 429.
 8.
Thomas S. Davies, “Answers to the mathematical questions,” The Leeds Correspondent 2 (1817): 265–292; Thomas T. Wilkinson, “Memoir of the literary labours of the late Professor Davies, F.R.S., F.R.A.S., &c.,” The Civil Engineer and Architect’s Journal 14 (1851), 77–78, on p. 77.
 9.
Thomas S. Davies, “Practical geometry,” Mechanics’ Magazine 3 (1825), 70–75, on p. 75.
 10.
Anon., “English mathematical literature,” The Westminster and Foreign Quarterly Review 55 (1851), 70–83, on p. 73.
 11.
Simson’s edition of Euclid, which was first published in Latin in 1756 and later in English, appeared in many editions well into the nineteenth century.
 12.
Joseph Hunter in his history of the BLSI describes Davies as being one of the stalwarts of the Association of the BLSI (the department of the BLSI responsible for public lectures). Joseph Hunter, The Connection of Bath with the Literature and Science of England (Bath & London, 1853), 19. Davies certainly gave lectures on ‘The Authority of Common Sense in Philosophical Inquiries’ (18 April 1831) and on ‘Comets’ (17 April 1832) since these were reported in the The Bath Chronicle and Weekly Gazette for 21 April 1831 and 19 April 1832, respectively, where he is referred to as ‘the Secretary’. On his election to the Royal Society of London, the same newspaper described him as ‘our learned townsman’ (25 April 1833).
 13.
Francis Ellis was elected to the Astronomical Society of London in 1828. He was proposed for election by Francis Bailey, immediate past President of the Society, who was one of the leading figures of his day in English astronomy.
 14.
Among Davies’s signatories for his election to the Royal Society was Dr. William Somerville, husband of Mary Somerville with whom Davies corresponded from 28 June 1832 to 4 February 1837. Bodleian Library Special Collections, Dep.c.370.MSD1.2. I am grateful to Brigitte Stenhouse for sharing transcriptions of this correspondence with me.
 15.
On 8 April 1833, Ellis noted in his journal ‘Read Whewell with Mr. Davies—whose jealousy of Airey [sic] is very curious. There is a morbid love of “fame” the ignis fatuus of “noble minds” about him, which joined with gall & bitterness against an exclusive body makes him always depreciate what is done at Cambridge’.
 16.
These are direct quotes from Davies which Ellis transcribed into his journal (1 July 1833). Davies was one of five hundred invited to the great dinner at Trinity College.
 17.
Davies was on firsthand terms with Thomas Leybourn, the editor of Leybourn’s Repository, meeting him when he visited Bath in the summer of 1830 (23 June 1830).
 18.
Thomas S. Davies. “Properties of the trapezium,” Philosophical Magazine 68 (1826): 116–125; Thomas S. Davies. “Properties of Pascal’s hexagramme mystique,” Philosophical Magazine 68 (1826): 333–339.
 19.
Thomas S. Davies, “An inquiry into the geometrical character of the HourLines upon the antique SunDials,” Transactions of the Royal Society of Edinburgh 12 (1834): 77–122; Thomas S. Davies. “On the equations of Loci traced upon the surface of a Sphere, as expressed by sphericalcoordinates,” Transactions of the Royal Society of Edinburgh 12 (1834): 259–362, 379–428.
 20.
John R. Young, Elements of Plane and Spherical Trigonometry, with its application to the principles of Navigation and Nautical Astronomy. With the Logarithmic and Trigonometrical Tables. To which is added some original Researches in Spherical Geometry, by T.S. Davies (London, 1833), 144. For biographical details about Logan, see Lukas M. Verburgt, “Robert Leslie Ellis, William Whewell and Kant: the role of Rev. H F C Logan,” BSHM Bulletin 31 (2016): 47–51.
 21.
Sophia De Morgan, Memoir of Augustus De Morgan (London: Longmans, Green & Co., 1882), 103.
 22.
The education at the Royal Military Academy had a strong emphasis on mathematics and many notable mathematicians were employed there during the nineteenthcentury, including, among others, Olinthus Gregory, James Joseph Sylvester and George Greenhill.
 23.
Davies provided an explanation for the ‘scattering’ of his writings in his article “University and nonuniversity mathematicians,” Mechanics’ Magazine 46 (1847): 428–431.
 24.
The obituaries of Davies are fulsome in their praise of him as a geometer, describing him as ‘a geometer of surpassing excellence’ (Jo. Cockle, Ja. Cockle “The late Professor Davies,” Mechanics’ Magazine 55 (1851): 432–433, on p. 432) and ‘the first of British geometers’ (Anon. “English mathematical literature”, 83). However, much of Davies’s work was concerned with solving problems arising from classical Greek geometry and he was not responsible for any major discoveries. That said, he was familiar with the recent work of Continental mathematicians, such as the projective geometry of Poncelet, and his work was known on the Continent. When the French mathematician, Michel Chasles (1793–1880), one of the leading geometers in France, visited England, he made a point of visiting Davies and presented him with a copy of his renowned Aperçu historique sur l’origine et le développement des méthodes en géométrie (1837) (Cockle & Cockle, “The late Professor Davies,” 432). A detailed description of Davies’s publications is given in Anon., “English mathematical literature”.
 25.
Thomas S. Davies, “Geometrical investigations concerning the phenomena of terrestrial magnetism,” Philosophical Transactions of the Royal Society 125 (1835): 221–248; Thomas S. Davies, “Geometrical investigations concerning the phenomena of terrestrial magnetism. Second series: – On the number of points at which a magnetic needle can take a position vertical to the Earth’s surface,” Philosophical Transactions of the Royal Society 126 (1836): 75–106. Thomas Stephens Davies correspondence with Mary Somerville, Bodleian Library Special Collections, Dep.c.370.MSD1.2.
 26.
Charles Hutton was professor of mathematics at the Royal Military Academy, Woolwich (1773–1807). His popular Course of Mathematics was first published in 1798. Davies, in his preface to the second volume, announced that ‘there is not a single line of the original work which has not been recomposed’. Charles Hutton, Course of Mathematics. Vol. 2. (London: Longman & Co., 1843), iii.
 27.
On the 24 December 1831, when Davies neither appeared nor sent a message, Ellis described him as ‘the most disagreeable creature extant’.
 28.
In connection with a visit to Bath of the mathematician Thomas Leybourn, Ellis reported that a friend at the BLSI had told him that Leybourn was ‘more boorish’ than Davies and had ‘even greater pretention to being a gentleman’ (7 June 1833).
 29.
In a paper published in 1844, Davies described Ellis as his ‘old friend and former pupil’ referring both to a paper of Ellis’s of 1841 and to correspondence with Ellis. The mathematics in question concerned the wellknown geometrical theorems and porisms of Matthew Stewart, professor of mathematics in Edinburgh (1747–1785), which had been published in 1746. Thomas S. Davies, “An analytical discussion of Dr. Matthew Stewart’s general theorems,” Transactions of the Royal Society of Edinburgh 15 (1844): 573–608, on p. 605. Robert Leslie Ellis, “Analytical demonstrations of Dr. Matthew Stewart’s Theorems,” Cambridge Mathematical Journal 2 (1841): 271–276. Reprinted in William Walton, ed. The Mathematical and Other Writings of Robert Leslie Ellis (Cambridge: Deighton, Bell & Co., 1863), 12–37.
 30.
Legendre’s Elements of Geometry and Trigonometry (1794), which was a reworking and extension of Euclid’s Elements into a more accessible form, was ‘highly esteemed in every part of Europe’. AdrienMarie Legendre, Elements of Geometry and Trigonometry (Edinburgh, 1822), v. It was translated into English in 1822 by Thomas Carlyle with editorial input from David Brewster, and by the time the English translation had gone to press the 12th French edition was in preparation. Ellis’s father maintained a continuing interest in his son’s mathematical activities. See, for example, Ellis’s journal entry for 19 December 1830 concerning the drawing of an ellipse.
 31.
Two years later, on 29 May 1830, he reflected on this entry, ‘This is the third anniversary of writing my journal. It was a pretty composition, but my first anniversary was much more grand, ‘O white poney [sic] and cliffs, O Legendre’. I never read it without appending to it, “O ass, why didst thou write such stuff?”’. For full journal entry for 29 May 1830, see Stray’s chapter in the present volume.
 32.
Hamilton’s was the first analytical geometry book in English to include geometry in three dimensions. See Alex D.D. Craik, “Henry Parr Hamilton (1794–1880) and analytical geometry at Cambridge”, BSHM Bulletin: Journal of the British Society for the History of Mathematics 35 (2020): 162–170.
 33.
Ellis very much liked the fact that the diagrams were on the same page as the subject they illustrated; many textbooks of the period put diagrams together at the back of the book since this was easier and cheaper to print.
 34.
Ellis had tutors for both French and German. See Stray’s chapter in the present volume.
 35.
Meier Hirsch (1765–1851) was a private teacher whose textbooks were very popular in Germany. His attempts to find a general solution to polynomial equations led to mental illness from which he never recovered. Moritz Cantor in his biographical article on Hirsch wrote ‘we must not put Hirsch in the same category as writers who think that they have found squaring of the circle, the perpetual motion machine and such like in our century. Hirsch lost mind over his task: those others had no mind to lose’, in Allgemeine Deutsche Biographie 12 (1880) 467–468, on p. 468. I am grateful to Reinhard SiegmundSchultze for alerting me to this quote.
 36.
Wright had studied at Cambridge and, although he was destined for a high position in the Tripos in 1819, an unlucky set of circumstances meant he was awarded only a pass degree. He published several textbooks designed for Cambridge preparation as well as a detailed account of his undergraduate experience. J.M.F. Wright. Alma Mater; or Seven Years at the University of Cambridge (London, 1827). For further details about Wright, see Andrew Warwick, Masters of Theory: Cambridge and the Rise of Mathematical Physics (Chicago & London: The University of Chicago Press, 2003), 69–72.
 37.
J.M.F. Wright. SelfExaminations in Algebra (London, 1825), 243.
 38.
Nothing further is known about P.B. Duncan.
 39.
Trisecting the angle is one of the three classical problems of Greek antiquity, the other two being duplicating the cube and squaring the circle. In each case a construction using only a straight edge and compasses was desired and many mathematicians provided many false proofs, with angle trisection being a particular favourite. In 1837 Pierre Wantzel proved the impossibility of trisecting the angle and duplicating the cube, see Jesper Lützen, “Why was Wantzel overlooked for a century? The changing importance of an impossibility result,” Historia Mathematica 36 (2009): 374–394. Almost fifty years later, in 1882, Ferdinand Lindemann proved that the number π is transcendental and thereby proved that squaring the circle is impossible. See Alfred Burton, “Angle trisection,” United Service Journal 1831 (Part 2): 406–408; 1831 (Part 3): 392–394.
 40.
Of ‘the numerous demonstrations’ on angle trisection received by the United Service Journal, only ‘the most concise’ were published, and none of the authors were identified by name. These short articles appeared in the issue for 1832 (Part 1), 398–400. The same issue carried a longer article on the subject which also came in for criticism: Major W. Mitchell, “On the trisection of an angle, and the mathematical principles of field movements,” United Service Journal 1832 (Part 1): 106–109.
 41.
L.P.V.M. Azemar, Trisection de l’angle, par L.P.V.M. Azemar, suivie de recherches analytiques sur le même sujet, par J.G. Garnier (Paris, 1809).
 42.
Thomas S. Davies, “New researches in spherical trigonometry,” Leybourn’s Mathematical Repository 6, Part 2 (1835): 168–188, on p. 172.
 43.
Carl G.J. Jacobi, “On certain properties of plane triangles which are not generally known.” Leybourn’s Mathematical Repository 6, Part 3 (1835): 68–96.
 44.
Ellis’s model of bees’ cells had been prompted by reading Daniel Cresswell’s Elementary Treatise on the Geometrical and Algebraical Investigation of Maxima and Minima (1817), 273–298. Ellis returned to the study of bees’ cells later in life and a manuscript, ‘On the form of bees’ cells’, which can be dated to sometime during or after 1843, was published posthumously in William Walton, ed. The Mathematical and other writings of Robert Leslie Ellis (Cambridge: Deighton, Bell & Co., 1863), 353–357.
 45.
For information about Addams, see Nicholas J. Wade, “Pursuing paradoxes posed by the waterfall illusion,” Perception 47 (2018): 689–693, on p. 691.
 46.
For an account of an auditory sensation experienced by Francis Ellis while bathing in a large warm bath, see Francis Ellis, “On the propagation of sound through unelastic fluids,” The Journal of Natural Philosophy, Chemistry and the Arts 25 (1810): 188.
 47.
The National Gallery of Practical Science was the brainchild of Jacob Perkins, the American inventor and physicist. For a description of the Gallery’s opening night see “Fashionable World,” The Morning Post (12 June 1832), on p. 3. Ellis visited it again with his father on 31 January 1840.
 48.
For a picture and description of Faraday’s apparatus, see: https://www.rigb.org/ourhistory/iconicobjects/iconicobjectslist/faradaymagneticspark
 49.
Charles Babbage, On the Economy of Machinery and Manufactures (London: Charles Knight, 1832).
 50.
Peacock’s other major works on algebra were his Report for the BAAS (1833) and a second, enlarged and revised, edition of his 1830 textbook published in two volumes (1842–45).
 51.
The ‘principle of the permanency of equivalent forms’ enables results from arithmetical algebra to be transferred into symbolical algebra. For discussions of Peacock’s work on algebra, see Helena M. Pycior, “George Peacock and the British origins of symbolical algebra,” Historia Mathematica 8 (1981): 23–45; Kevin Lambert, “A natural history of mathematics. George Peacock and the making of English algebra,” Isis 104 (2013): 278–302; Lukas M. Verburgt, “Duncan F. Gregory, William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction,” Annals of Science 73:1 (2016): 40–67.
 52.
George Peacock, A Treatise on Algebra (Cambridge, 1830), xxiii.
 53.
Lacroix’s Traité, which was an abridged version of his threevolume work (1797–1800), was translated into English by Charles Babbage, John Herschel and George Peacock (1816) for the use of students at Cambridge. For a discussion of the contents of the Lacroix’s original text, see João C. Domingues, “S.F. Lacroix, Traité du Calcul Différentiel et du Calcul Intégral, First Edition (1797–1800),” in Ivor GrattanGuinness, ed., Landmark Writings in Western Mathematics 1640–1940 (Amsterdam: Elsevier, 2005), 277–291.
 54.
Challis, Senior Wrangler of 1825, who had had to resign his Fellowship on his marriage in 1831, was appointed to the Plumian chair in 1836. He was Rector of Papworth Everard from 1830 to 1852. Today he is best remembered for failing to identify the planet Neptune in 1846.
 55.
The reading list consisted of some 40 to 50 books, mostly related to classics, reflecting the type of tuition that Ellis would receive. See Stray and Crilly in this volume for details of Challis’s tutoring.
 56.
John Crowfoot was 12th wrangler in 1839. Ellis met with him again at Cambridge. Barrett was most likely Samuel Barrett who entered Queens’ College in 1834, migrated to Pembroke College in 1835, and graduated B.A. in 1839.
 57.
Harvey Goodwin, “Biographical memoir of Robert Leslie Ellis, M.A.,” in Walton, Ellis, ixxxxvi, on p. xiv.
 58.
For a history of the Tripos examination and a discussion of its emphasis on mathematics, see John Gascoigne, “Mathematics and meritocracy: The emergence of the Cambridge Mathematical Tripos,” Social Studies of Science 14 (1984): 547–584.
 59.
An analysis of the careers of senior wranglers is given in C.M. Neale, The Senior Wranglers of the University of Cambridge from 1748 to 1907 (Cambridge, 1907), a book published the year the order of merit was abolished. For an indication of the significance attached to being senior wrangler in 1840, see the anonymous short story “Tales of our University I: A Legend for Senior Wranglers,” The Cambridge University Magazine 1 (1840): 59–69.
 60.
Whewell set out his ideas in ‘Thoughts on the Study of Mathematics as Part of a Liberal Education’ in 1837 to which he added further remarks in On the Principles of English University Education, of which a second edition appeared in 1838. For a discussion of Whewell’s influence on Cambridge mathematics, see Harvey W. Becher, “William Whewell and Cambridge mathematics,” Historical Studies in Physical Sciences 11 (1980): 1–48.
 61.
Goodwin, “Biographical memoir,” xiv. Woodhouse’s historical treatise on the calculus of variations was the first booklength treatment in English of the subject and is notable for its use of continental notation. Woodhouse, who held the Lucasian and Plumian chairs during the 1820s, provided the initial stimulus for the reform of British mathematics in the early nineteenth century and his publications, especially Principles of Analytical Calculation (1803) which introduced notions of the Lagrangian calculus, were influential in Cambridge. See Niccolò Guicciardini, The Development of the Newtonian Calculus in Britain 1700–1800 (Cambridge: Cambridge University Press, 1989), 126–131.
 62.
See the comment about Woodhouse’s book in George Biddell Airy, Mathematical Tracts on the Lunar and Planetary Theories, the Figure of the Earth, Precession and Nutation, the Calculus of Variations and the Undulatory Theory of Optics (Cambridge, 1826), vii.
 63.
Peacock’s lectures were advertised as ‘Science of astronomy and practical methods of observation; use of Instruments. Geometry, and general principles of Mathematical Reasoning’. Challis’ lectures were published as Syllabus of a Course of Experimental Lectures on the Equilibrium and Motion of Fluids and on Optics (Cambridge, 1838).
 64.
Goodwin, “Biographical memoir,” xv.
 65.
Goodwin, “Biographical memoir,” xv.
 66.
R.E. Anderson (revised by Maria Panteki). “John Hymers (1803–1887),” Oxford Dictionary of National Biography (2004), doi: https://doi.org/101093/ref:odnb/14340
 67.
Anon., “Scientific morality at Cambridge,” Mechanics’ Magazine 46 (1847): 317–321.
 68.
See William Whewell, On the Free Motion of Points, and on Universal Gravitation, Including the Principal Propositions of Books I and III of the Principia; the First Part of a New Edition of a Treatise on Dynamics (Cambridge, 1832), v; Mary Somerville and Martha Somerville, Personal Recollections, from Early Life to Old Age of Mary Somerville (London, 1873), 172.
 69.
For a full discussion of Hopkins as a coach, including descriptions of the experience of being coached by him, see Alex D.D. Craik, Mr Hopkins’ Men: Cambridge Reform and British Mathematics in the nineteenth Century (London: Springer, 2008).
 70.
Warwick, Masters of Theory, 84–85.
 71.
Warwick, Masters of Theory, 84.
 72.
The Gentleman’s Magazine (1866), 706, quoted in Tony Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age (Baltimore: Johns Hopkins University Press, 2006), 40.
 73.
Goodwin, “Biographical memoir,” xv.
 74.
In contrast to Ellis, George Gabriel Stokes, Senior Wrangler of 1841 (the year after Ellis), thrived under the system. See June BarrowGreen, “Stokes’s mathematical education,” Philosophical Transactions of the Royal Society A 378:2174 (2020), doi: https://doi.org/10.1098/rsta.2019.0506
 75.
See the diary entry for 15 May 1839. In 1852 Hopkins estimated that to a good student the cost of private tutoring for three years was approximately £150 (excluding additional coaching in the vacation). He was thus earning something in region of £750 a year through his coaching, a substantial amount and a sum much higher than the stipend of most of the university professors (Craik, Mr Hopkins’ Men, 100).
 76.
Stokes’s notes cover several different subjects, mostly in applied mathematics or mathematical physics. MSS Stokes Collection, PA 2–24, CUL, Manuscripts and University Archives. An idea of Hopkins’s views on mathematics and what informed his teaching can be gleaned from a pamphlet he wrote in 1841 attacking proposals to reform the Tripos: William Hopkins. Remarks on Certain Proposed Regulations Respecting the Studies of the University and the Period of Conferring the Degree of B.A. (Cambridge, 1841). For Hopkins mathematics was important because it unlocked the secrets of the universe, and these proposals, which advocated the exclusion of various topics in applied mathematics, were not at all to his taste. Hopkins’s pamphlet also provided a response to a recent attack by Peacock on private tutoring: George Peacock, Observations on the Statutes of the University of Cambridge (London, 1841). For discussions of the contents of the pamphlets by Peacock and Hopkins, see Craik, Mr Hopkins’ Men, 67–69, 114–116.
 77.
William Hopkins, Elements of Trigonometry (London, 1833).
 78.
Sir George Smith Gibbes was a physician who practised in Bath and who gave the inaugural address at the opening of the BLSI in 1825. He earned his knighthood for being physician to Queen Charlotte, wife of King George III. The reference to ‘the air pump and the electrical machine’ is a reference to scientific instruments being used for show (see note 47). Ellis mentions Gibbes several times in his journal indicating that he was wellknown to the family.
 79.
Lorraine Skrine was the daughter of the banker Julian Skrine. Ellis was ‘surprised to find her a ladylike and affectionate girl’. In 1844 she married Robert Phelps (5W 1833) Master of Sidney Sussex College and twice ViceChancellor of the University. It was reported that Phelps ‘looked into everything about the house & is a capital hand at frying an omelet – Mrs. Phelps can’t even keep the laundress’s accounts’. See, John A. Venn, “Robert Phelps,” Alumni Cantabrigienses: A Biographical List of All Known Students, Graduates and Holders of Office at the University of Cambridge, from the Earliest Times to 1900. Part II from 1752–1900. Vol. V. (Cambridge: Cambridge University Press, 1922–1954).
 80.
Of the attendees on 29 April 1839, the others listed by Ellis were Matthew O’Brien (3W 1838), John Ball (41W 1839) and Goodwin, the latter being the only other undergraduate.
 81.
Goodwin, “Biographical memoir,” xv.
 82.
For the full journal entry for 8 February 1839, when Ellis is expressing these feelings, see Stray’s chapter.
 83.
During the nineteenth century, the examination went through many reforms. 1840 was the first year in which the examination lasted for six days, an extra day having been added to that of the previous year. A detailed discussion of the development and content of the examination is given in Warwick, Masters of Theory.
 84.
Goodwin, “Biographical memoir,” xix. Usually the Moderators and Examiners were recent wranglers, and usually at least one of the Moderators continued as either a Moderator or an Examiner in the following year, thereby ensuring continuity. Ellis himself would be a Moderator in 1844 and an Examiner in 1845. Moderators sometimes published solutions of the Tripos problems and Ellis, together with his fellow Moderator, Matthew O’Brien, did so in 1844. Robert L. Ellis, Matthew O’Brien. The SenateHouse Problems for 1844 with Solutions (Cambridge, 1844).
 85.
Smith was one of the founders of the Cambridge Mathematical Journal, a journal to which Ellis contributed and sometime edited. See Crilly’s chapter in this volume.
 86.
Until 1850 students who had not obtained honours in the Mathematical Tripos were not allowed to sit the Classical Tripos. It was therefore possible for highachieving classics students to fail to get a degree. In 1841, several of the best classics students from Trinity were spun out in this way resulting in a public uproar and a loud clamour for reform, see Christopher Stray, “The slaughter of 1841: Mathematics and Classics in early Victorian Cambridge,” History of Universities 34 (2021), forthcoming.
 87.
Charles A. Bristed, Five Years in an English University (New York, 1852), 331.
 88.
Bristed, Five Years in an English University, 126.
 89.
Bristed, Five Years in an English University, 163.
 90.
Peacock, Observations on the Statutes of the University of Cambridge, 153. Although there were several reforms of the Tripos during the nineteenth century, the artificiality of the problems persisted. Max Born recalled how the students in Göttingen at the beginning of the twentieth century made fun of the Cambridge problems by inventing one for themselves: “On an elastic bridge stands an elephant of negligible mass, on its trunk stands a mosquito of mass m. Calculate the vibrations on the bridge when the elephant moves the mosquito by rotating its trunk”. Max Born, My Life. Recollections of a Nobel Laureate (1978), 282.
 91.
Robert Leslie Ellis, “On the method of least squares,” Transactions of the Cambridge Philosophical Society 8 (1844): 204–219. Reprinted in Walton, Ellis, 12–37. See Stigler in the present volume for an account of Ellis’s work in probability theory.
 92.
Quoted in Hardwicke D. Rawnsley, Harvey Goodwin, Bishop of Carlisle: A Biographical Memoir (London, 1896), 45. Goodwin, who later became Bishop of Carlisle, had little contact with Ellis when they were students but came to know him well afterwards.
 93.
Goodwin, “Biographical memoir,” xvi.
 94.
Letter from Robert Leslie Ellis to Lady Affleck, 17 January 1840, TCL, Add.MS.a.81/69.
 95.
Bristed, Five Years in an English University, 326.
 96.
Ellis followed Peacock’s advice and was elected to a Fellowship of Trinity in October 1840. Since graduates could sit the Fellowship examination three times and the examiners often favoured someone who was on their final attempt, to be elected on a first attempt was quite unusual.
 97.
Ellis’s Trinity friends fared variably in the Tripos. Alexander Gooden just scraped into the second class. His goal was the Classical Tripos and two months later he emerged as one of two Senior Classics. He died of peritonitis the following year. For details of his life and of Cambridge in the 1830s, see Jonathan Smith and Christopher A. Stray, eds. Cambridge in the 1830s: The Letters of Alexander Chisholm Gooden (Woodbridge: Boydell, 2003). Tom Taylor was 18th in the third class. Ellis considered him eccentric but liked and admired him. After a brief spell as Professor of English at University College London, Taylor made a career as a successful dramatist and editor of Punch. Walter Cockburn was seventh in the second class, and Richard Mate was 14th wrangler.
 98.
It was customary for each candidate to be presented by a Fellow of his college. In Ellis’s year, the Fellow for Trinity was Thomas Burcham.
 99.
Ellis maintained his friendship with Hume after graduation. Hume’s father was a doctor and a Radical MP, and he was well connected scientifically. On 24 May 1840, Ellis records meeting Charles Babbage and Charles Wheatstone at a dinner with the Humes in London.
 100.
Esquire Bedell to the University is a partly administrative and partly ceremonial post. See Henry P. Stokes, The Esquire Bedells of the University of Cambridge from the thirteenth Century to the twentieth Century (Cambridge: Cambridge Antiquarian Society, 1911).
 101.
Rawnsley, Harvey Goodwin, 47.
 102.
For a discussion of the origin and development of the Smith’s Prizes, together with a list of winners up to 1940, see June BarrowGreen, “‘A Correction to the Spirit of Too Exclusively Pure Mathematics’: Robert Smith (1689–1768) and his prizes at Cambridge University,” Annals of Science 56 (1999): 271–316.
 103.
Miller had solid mathematics credentials having been fifth wrangler in 1826 and the author of Cambridge textbooks on hydrostatics and hydrodynamics (1831) and the calculus (1833). He had been elected to the Chair of Mineralogy in 1834 in succession to Whewell.
 104.
Rawnsley, Harvey Goodwin, 48. Woolly later made a name for himself as a naval architect.
 105.
Although no senior wrangler attained such high office, these two positions seem to have been a popular aspiration. The following year, Stokes, after his success, was told he had only to determine whether he would be one of them or Prime Minister of England (BarrowGreen, “Stokes’s mathematical education,” 13).
 106.
For further details of Ellis’s mathematical work, and his relationship with the Cambridge Mathematical Journal, see Crilly’s chapter in the present volume.
 107.
Robert Leslie Ellis, “On some properties of the parabola”, Cambridge Mathematical Journal 1 (1839): 204–208. Reprinted in Walton, Ellis, 63–67.
 108.
Anon. [Forbes], “Robert Leslie Ellis,” The Athenaeum 1685 (1860): 205–206, on p. 205.
 109.
For Ellis’s works, see Appendix 1 (‘Bibliography of Ellis’s Writings’). Primary works mentioned only briefly in the footnotes to Part and Part II but not quoted or discussed are not included in the bibliography below; their complete bibliographic information is provided in the notes themselves.
Bibliography
For Ellis’s works, see Appendix 1 (‘Bibliography of Ellis’s Writings’). Primary works mentioned only briefly in the footnotes to Part and Part II but not quoted or discussed are not included in the bibliography below; their complete bibliographic information is provided in the notes themselves.
Davies, Thomas S. 1835b. Geometrical investigations concerning the phenomena of terrestrial magnetism. Philosophical Transactions of the Royal Society 125: 221–248.
———. 1836. Geometrical investigations concerning the phenomena of terrestrial magnetism. Second series – On the number of points at which a magnetic needle can take a position vertical to the Earth’s surface. Philosophical Transactions of the Royal Society 126: 75–106.
Woodhouse, Robert. 1810. A Treatise on Isoperimetrical Problems, and the Calculus of Variations. Cambridge.
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BarrowGreen, J. (2022). “A Senior Wrangler Among Senior Wranglers”: The Mathematical Education of Robert Leslie Ellis. In: Verburgt, L.M. (eds) A Prodigy of Universal Genius: Robert Leslie Ellis, 18171859. Studies in History and Philosophy of Science, vol 55. Springer, Cham. https://doi.org/10.1007/9783030852580_2
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