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.

"I may fix upon this as the time when my daily habits were settled in the form in which they continued for several years. I rose in time for the chapel service at 7. It was the College regulation that every student should attend Chapel four mornings and four evenings (Sunday being one of each) in every week: and in this I never failed. After chapel service I came to my lodgings and breakfasted. At 9 I went to College lectures, which lasted to 11. Most of my contemporaries, being intended for the Church, attended also divinity lectures: but I never did. I then returned, put my lecture notes in order, wrote my piece of Latin prose, and then employed myself on the subject which I was reading for the time: usually taking mathematics at this hour. At 2 or a little sooner I went out for a long walk, usually 4 or 5 miles into the country: sometimes if I found companions I rowed on the Cam (a practice acquired rather later). A little before 4 I returned, and at 4 went to College Hall. After dinner I lounged till evening chapel time, 1/2 past 5, and returning about 6 I then had tea. Then I read quietly, usually a classical subject, till 11; and I never, even in the times when I might seem most severely pressed, sat up later.

"From this time to the close of the annual examination (beginning of June) I remained at Cambridge, stopping there through the Easter Vacation. The subjects of the mathematical lectures were ordinary algebra and trigonometry: but Mr Peacock always had some private problems of a higher class for me, and saw me I believe every day. The subjects of the Classical lectures were, the termination of Hippolytus, the book of Thucydides and the oration of Cicero. In mathematics I read Whewell's Mechanics, then just published (the first innovation made in the Cambridge system of Physical Sciences for many years): and I find in my scribbling-paper notes, integrals, central forces, Finite Differences, steam-engine constructions and powers, plans of bridges, spherical trigonometry, optical calculations relating to the achromatism of eye-pieces and achromatic object-glasses with lenses separated, mechanical problems, Transit of Venus, various problems in geometrical astronomy (I think it was at this time that Mr Peacock had given me a copy of Woodhouse's Astronomy 1st Edition), the rainbow, plans for anemometer and for a wind-pumping machine, clearing lunars, &c., with a great number of geometrical problems. I remark that my ideas on the Differential Calculus had not acquired on some important points the severe accuracy which they acquired in a few months. In Classics I read the Persae of Aeschylus, Greek and Roman history very much (Mitford, Hooke, Ferguson) and the books of Thucydides introductory to that of the lecture subject (the 3rd): and attended to Chronology. On the scribbling-paper are verse-translations from Euripides, careful prose-translations from Thucydides, maps, notes on points of grammar &c. I have also little MS. books with abundant notes on all these subjects: I usually made a little book when I pursued any subject in a regular way.

"On May 1st Mr Dobree, the head lecturer, sent for me to say that he appointed me head-lecturer's Sizar for the next year. The stipend of this office was £10, a sum upon which I set considerable value in my anxiety for pecuniary independence: but it was also gratifying to me as shewing the way in which I was regarded by the College authorities.

"On Wednesday, May 24th, 1820, the examination began. I was anxious about the result of the examination, but only in such a degree as to make my conduct perfectly steady and calm, and to prevent me from attempting any extraordinary exertion.

"When the Classes were published the first Class of the Freshman's Year (alphabetically arranged, as is the custom) stood thus: Airy, Boileau, Childers, Drinkwater, Field, Iliff, Malkin, Myers, Romilly, Strutt, Tate, Winning. It was soon known however that I was first of the Class. It was generally expected (and certainly by me) that, considering how great a preponderance the Classics were understood, in the known system of the College, to have in determining the order of merit, Field would be first. However the number of marks which Field obtained was about 1700, and that which I obtained about 1900. No other competitor, I believe, was near us."—In a letter to Airy from his College Tutor, Mr J. D. Hustler, there is the following passage: "It is a matter of extreme satisfaction to me that in the late examination you stood not only in the First Class but first of the first. I trust that your future exertions and success will be commensurate with this honourable beginning."

"Of the men