"I was set down at the Hoop, saw Trinity College for the first time, found Mr Hustler, was conducted by his servant to the robe-maker's, where I was invested in the cap and blue gown, and after some further waiting was installed into lodgings in Bridge Street. At 4 o'clock I went to the College Hall and was introduced by Mr Hustler to several undergraduates, generally clever men, and in the evening I attended Chapel in my surplice (it being St Luke's day) and witnessed that splendid service of which the occasional exhibition well befits the place.
"As soon as possible, I called on Mr Peacock, Mr Musgrave, and Professor Sedgwick. By all I was received with great kindness: my examination papers had been sent to them, and a considerable reputation preceded me. Mr Peacock at once desired that I would not consider Mr C. Musgrave's letter as an ordinary introduction, but that I would refer to him on all occasions. And I did so for several years, and always received from him the greatest assistance that he could give. I think that I did not become acquainted with Mr Whewell till the next term, when I met him at a breakfast party at Mr Peacock's. Mr Peacock at once warned me to arrange for taking regular exercise, and prescribed a walk of two hours every day before dinner: a rule to which I attended regularly, and to which I ascribe the continuance of good general health.
"I shewed Mr Peacock a manuscript book which contained a number of original Propositions which I had investigated. These much increased my reputation (I really had sense enough to set no particular value on it) and I was soon known by sight to almost everybody in the University. A ridiculous little circumstance aided in this. The former rule of the University (strictly enforced) had been that all students should wear drab knee-breeches: and I, at Mr Clarkson's recommendation, was so fitted up. The struggle between the old dress and the trowsers customary in society was still going on but almost terminated, and I was one of the very few freshmen who retained the old habiliments. This made me in some measure distinguishable: however at the end of my first three terms I laid these aside.
"The College Lectures began on Oct. 22: Mr Evans at 9 on the
Hippolytus, and Mr Peacock at 10 on Euclid (these being the Assistant
Tutors on Mr Hustler's side): and then I felt myself established.
"I wrote in a day or two to my uncle Arthur Biddell, and I received from him a letter of the utmost kindness. He entered gravely on the consideration of my prospects, my wants, &c.: and offered at all times to furnish me with money, which he thought my father's parsimonious habits might make him unwilling to do. I never had occasion to avail myself of this offer: but it was made in a way which in no small degree strengthened the kindly feelings that had long existed between us.
"I carefully attended the lectures, taking notes as appeared necessary. In Mathematics there were geometrical problems, algebra, trigonometry (which latter subjects the lectures did not reach till the terms of 1820). Mr Peacock gave me a copy of Lacroix's Differential Calculus as translated by himself and Herschel and Babbage, and also a copy of their Examples. At this time, the use of Differential Calculus was just prevailing over that of Fluxions (which I had learnt). I betook myself to it with great industry. I also made myself master of the theories of rectangular coordinates and some of the differential processes applying to them, which only a few of the best of the university mathematicians then wholly possessed. In Classical subjects I read the Latin (Seneca's) and English Hippolytus, Racine's Phèdre (which my sister translated for me), and all other books to which I was referred, Aristotle, Longinus, Horace, Bentley, Dawes &c., made verse translations of the Greek Hippolytus, and was constantly on the watch to read what might be advantageous.
"Early in December Mr Hustler sent for me to say that one of the Company of Fishmongers, Mr R. Sharp, had given to Mr John H. Smyth, M.P. for Norwich, the presentation to a small exhibition of £20 a year, which Mr Smyth had placed in Mr Hustler's hands, and which Mr Hustler immediately conferred on me. This was my first step towards pecuniary independence. I retained this exhibition till I became a Fellow of the College.
"I stayed at Cambridge during part of the winter vacation, and to avoid expense I quitted my lodgings and went for a time into somebody's rooms in the Bishop's Hostel. (It is customary for the tutors to place students in rooms when their right owners are absent.) I took with me Thucydides and all relating to it, and read the book, upon which the next term's lectures were to be founded, very carefully. The latter part of the vacation I spent at Bury, where I began with the assistance of my sister to pick up a little French: as I perceived that it was absolutely necessary for enabling me to read modern mathematics.
"During a part of the time I employed myself in writing out a paper on the geometrical interpretation of the algebraical expression sqrt(-1). I think that the original suggestion of perpendicular line came from some book (I do not remember clearly), and I worked it out in several instances pretty well, especially in De Moivre's Theorem. I had spoken of it in the preceding term to Mr Peacock and he encouraged me to work it out. The date at the end is 1820, January 21. When some time afterwards I spoke of it to Mr Hustler, he disapproved of my employing my time on such speculations. About the last day of January I returned to Cambridge, taking up my abode in my former lodgings. I shewed my paper on sqrt(-1) to Mr Peacock, who was much pleased with it and shewed it to Mr Whewell and others.
"On February 1 I commenced two excellent customs. The first was that I always had upon my table a quire of large-sized scribbling-paper sewn together: and upon this paper everything was entered: translations into Latin and out of Greek, mathematical problems, memoranda of every kind (the latter transferred when necessary to the subsequent pages), and generally with the date of the day. This is a most valuable custom. The other was this: as I perceived that to write Latin prose well would be useful to me, I wrote a translation of English into Latin every day. However much pressed I might be with other business, I endeavoured to write at least three or four words, but if possible I wrote a good many sentences.