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"I carefully attended the lectures, taking notes as appeared necessary. In Mathematics there were geometrical problems, algebra, trigonometry . 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 . 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 and English Hippolytus, Racine's Ph?dre , 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.

"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. 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. I think that the original suggestion of perpendicular line came from some book , 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 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 , 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 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 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 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 : 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 , 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 and the books of Thucydides introductory to that of the lecture subject : 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 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 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 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 whom I have named, Drinkwater was afterwards Legal Member of the Supreme Court of India, Field was afterwards Rector of Reepham, Romilly became Solicitor-General, Strutt became M.P. for Derby and First Commissioner of Railways, Tate was afterwards master of Richmond Endowed School, Childers was the father of Childers who was subsequently First Lord of the Admiralty.

"I returned to Bury immediately. While there, some students applied to me to take them as pupils, but I declined. This year of my life enabled me to understand how I stood among men. I returned to Cambridge about July 11th. As a general rule, undergraduates are not allowed to reside in the University during the Long Vacation. I believe that before I left, after the examination, I had made out that I should be permitted to reside: or I wrote to Mr Hustler. I applied to Mr Hustler to be lodged in rooms in College: and was put, first into rooms in Bishop's Hostel, and subsequently into rooms in the Great Court.

"The first affair that I had in College was one of disappointment by no means deserving the importance which it assumed in my thoughts. I had been entered a Sizar, but as the list of Foundation Sizars was full, my dinners in Hall were paid for. Some vacancies had arisen: and as these were to be filled up in order of merit, I expected one: and in my desire for pecuniary independence I wished for it very earnestly. However, as in theory all of the first class were equal, and as there were some Sizars in it senior in entrance to me, they obtained places first: and I was not actually appointed till after the next scholarship examination . However a special arrangement was made, allowing me to sit at the Foundation-Sizars' table whenever any of the number was absent: and in consequence I received practically nearly the full benefits.

"Mr Peacock, who was going out for the vacation, allowed me access to his books. I had also command of the University Library and Trinity Library: and spent this Long Vacation, like several others, very happily indeed.

"The only non-mathematical subjects of the next examination were The Gospel of St Luke, Paley's Evidences, and Paley's Moral and Political Philosophy. Thus my time was left more free to mathematics and to general classics than last year. I now began a custom which I maintained for some years. Generally I read mathematics in the morning, and classics for lectures in the afternoon: but invariably I began at 10 o'clock in the evening to read with the utmost severity some standard classics and at 11 precisely I left off and went to bed. I continued my daily translations into Latin prose as before.

"On August 24th, 1820, Rosser, a man of my own year, engaged me as private tutor, paying at the usual rate : and immediately afterwards his friend Bedingfield did the same. This occupied two hours every day, and I felt that I was now completely earning my own living. I never received a penny from my friends after this time.

"I find on my scribbling-paper various words which shew that in reading Poisson I was struggling with French words. There are also Finite Differences and their Calculus, Figure of the Earth , various Attractions , Integrals, Conic Sections, Kepler's Problem, Analytical Geometry, D'Alembert's Theorem, Spherical Aberration, Rotations round three axes , Floating bodies, Evolute of Ellipse, Newton's treatment of the Moon's Variation. I attempted to extract something from Vince's Astronomy on the physical explanation of Precession: but in despair of understanding it, and having made out an explanation for myself by the motion round three axes, I put together a little treatise which with some corrections and additions was afterwards printed in my Mathematical Tracts. On Sept. 14th I bought Woodhouse's Physical Astronomy, and this was quite an epoch in my mathematical knowledge. First, I was compelled by the process of "changing the independent variable" to examine severely the logic of the Differential Calculus. Secondly, I was now able to enter on the Theory of Perturbations, which for several years had been the desired land to me.

"At the Fellowship Election of Oct. 1st, Sydney Walker was elected Fellow. He then quitted the rooms in which he had lived , and I immediately took them. They suited me well and I lived very happily in them till I was elected Scholar. They are small rooms above the middle staircase on the south side of Neville's Court. I had access to the leads on the roof of the building from one of my windows. This was before the New Court was built: my best window looked upon the garden of the College butler.

"I had brought to Cambridge the telescope which I had made at Colchester, and about this time I had a stand made by a carpenter at Cambridge: and I find repeated observations of Jupiter and Saturn made in this October term.

"Other mathematical subjects on my scribbling-paper are: Geometrical Astronomy, Barometers , Maclaurin's Figure of the Earth, Lagrange's Theorem, Integrals, Differential Equations of the second order, Particular Solutions. In general mathematics I had much discussion with Atkinson , and in Physics with Rosser, who was a friend of Sir Richard Phillips, a vain objector to gravitation. In Classics I read Aeschylus and Herodotus.

"On October 5th I received notice from the Head Lecturer to declaim in English with Winning. On October 6th we agreed on the subject, "Is natural difference to be ascribed to moral or to physical causes?" I taking the latter side. I spoke the declamation on October 25th. On October 26th I received notice of Latin declamation with Myers: subject agreed on, "Utrum civitati plus utilitatis an incommodi afferant leges quae ad vitas privatorum hominum ordinandas pertinent"; I took the former. The declamation was recited on November 11, when a curious circumstance occurred. My declamation was rather long: it was the first Saturday of the term on which a declamation had been spoken: and it was the day on which arrived the news of the withdrawal of the Bill of Pains and Penalties against Queen Caroline. In consequence the impatience of the undergraduates was very great, and there was such an uproar of coughing &c. in the Chapel as probably was never known. The Master and Tutors and Deans tried in vain to stop the hubbub. However I went on steadily to the end, not at all frightened. On the Monday the Master sent for me to make a sort of apology in the name of the authorities, and letters to the Tutors were read at the Lectures, and on the whole the transaction was nowise disagreeable to me.

"On the Commemoration Day, December 15th, I received my Prize as First-Class man, after dinner in the College Hall. After a short vacation spent at Bury and Playford I returned to Cambridge, walking from Bury on Jan. 22nd, 1821. During the next term I find in Mathematics Partial Differential Equations, Tides, Sound, Calculus of Variations, Composition of rotary motions, Motion in resisting medium, Lhuillier's theorem, Brightness of an object as seen through a medium with any possible law of refraction , star-reductions, numerical calculations connected with them, equilibrium of chain under centripetal force , investigation of the magnitude of attractive forces of glass, &c., required to produce refraction. I forget about Mathematical Lectures; but I have an impression that I regularly attended Mr Peacock's lectures, and that he always set me some private problems.

"I attended Mr Evans's lectures on St Luke: and I find many notes about the history of the Jews, Cerinthus and various heresies, Paley's Moral Philosophy, Paley's Evidences, and Biblical Maps: also speculations about ancient pronunciations.

"For a week or more before the annual examination I was perfectly lazy. The Classes of my year were not published till June 11. It was soon known that I was first with 2000 marks, the next being Drinkwater with 1200 marks. After a short holiday at Bury and Playford I returned to Cambridge on July 18th, 1821. My daily life went on as usual. I find that in writing Latin I began Cicero De Senectute . Some time in the Long Vacation the names of the Prizemen for Declamations were published: I was disappointed that not one, English or Latin, was assigned to me: but it was foolish, for my declamations were rather trumpery.

"My former pupil, Rosser, came again on August 14th. On August 29th Dr Blomfield called, to engage me as Tutor to his brother George Beecher Blomfield, and he commenced attendance on Sept. 1st. With these two pupils I finished at the end of the Long Vacation: for the next three terms I had one pupil, Gibson, a Newcastle man, recommended by Mr Peacock, I believe, as a personal friend .

"The only classical subject appointed for the next examination was the 5th, 6th and 7th Books of the Odyssey: the mathematical subjects all the Applied Mathematics and Newton. There was to be however the Scholarship Examination .

"When the October term began Mr Hustler, who usually gave lectures in mathematics to his third-year pupils, said to me that it was not worth my while to attend his lectures, and he or Mr Peacock suggested that Drinkwater, Myers, and I should attend the Questionists' examinations. The Questionists are those who are to take the degree of B.A. in the next January: and it was customary, not to give them lectures, but three times a week to examine them by setting mathematical questions, as the best method of preparing for the B.A. examination. Accordingly it was arranged that we should attend the said examinations: but when we went the Questionists of that year refused to attend. They were reported to be a weak year, and we to be a strong one: and they were disposed to take offence at us on any occasion. From some of the scholars of our year who sat at table with scholars of that year I heard that they distinguished us as 'the impudent year,' 'the annus mirabilis' &c. On this occasion they pretended to believe that the plan of our attendance at the Questionists' examinations had been suggested by an undergraduate, and no explanation was of the least use. So the Tutors agreed not to press the matter on them: and instead of it, Drinkwater, Myers, and I went three times a week to Mr Peacock's rooms, and he set us questions. I think that this system was also continued during the next two terms or part of them, but I am not certain.

"At this time my poor afflicted father was suffering much from a severe form of rheumatism or pain in the legs which sometimes prevented him from going to bed for weeks together.

"On the Commemoration Day, Dec. 18th, I received my prize as first-class man in Hall again. The next day I walked to Bury, and passed the winter vacation there and at Playford.

"I returned to Cambridge on Jan. 24th, 1822. On Feb. 12th I kept my first Act, with great compliments from the Moderator, and with a most unusually large attendance of auditors. These disputations on mathematics, in Latin, are now discontinued. On March 20th I kept a first Opponency against Sandys. About this time I received Buckle, a Trinity man of my own year, who was generally supposed to come next after Drinkwater, as pupil. On my sheets I find integrals and differential equations of every kind, astronomical corrections , chances, Englefield's comets, investigation of the brightness within a rainbow, proof of Clairaut's theorem in one case, metacentres, change of independent variable applied to a complicated case, generating functions, principal axes. On Apr. 8th I intended to write an account of my eye: I was then tormented with a double image, I suppose from some disease of the stomach: and on May 28th I find by a drawing of the appearance of a lamp that the disease of my eye continued.

"On Feb. 11th I gave Mr Peacock a paper on the alteration of the focal length of a telescope as directed with or against the Earth's orbital motion which was written out for reading to the Cambridge Philosophical Society on Feb. 24th and 25th. On Feb. 1 my MS. on Precession, Solar Inequality, and Nutation, was made complete.

"The important examination for Scholarships was now approaching. As I have said, this one opportunity only was given to Sizars , and it is necessary to be a Scholar in order to be competent to be a candidate for a Fellowship. On Apr. 10th I addressed my formal Latin letter to the Seniors. There were 13 vacancies and 37 candidates. The election took place on Apr. 18th, 1822. I was by much the first and was complimented by the Master and others. Wrote the formal letter of thanks as usual. I was now entitled to claim better rooms, and I took the rooms on the ground floor on the East side of the Queen's Gate of the Great Court. Even now I think of my quiet residence in the little rooms above the staircase in Neville's Court with great pleasure. I took possession of my new rooms on May 27th.

"The Annual Examination began on May 30th. The Classes were published on June 5th, when my name was separated from the rest by two lines. It was understood that the second man was Drinkwater, and that my number of marks was very nearly double of his. Having at this time been disappointed of a proposed walking excursion into Derbyshire with a college friend, who failed me at the last moment, I walked to Bury and spent a short holiday there and at Playford.

"I returned to Cambridge on July 12th, 1822. I was steadily busy during this Long Vacation, but by no means oppressively so: indeed my time passed very happily. The Scholars' Table is the only one in College at which the regular possessors of the table are sure never to see a stranger, and thus a sort of family intimacy grows up among the Scholars. Moreover the Scholars feel themselves to be a privileged class 'on the foundation,' and this feeling gives them a sort of conceited happiness. It was the duty of Scholars by turns to read Grace after the Fellows' dinner and supper, and at this time I know it by heart. They also read the Lessons in Chapel on week days: but as there was no daily chapel-service during the summer vacation, I had not much of this. In the intimacy of which I speak I became much acquainted with Drinkwater, Buckle, Rothman, and Sutcliffe: and we formed a knot at the table for several years. During this Vacation I had for pupils Buckle and Gibson.

"I wrote my daily Latin as usual, beginning with the retranslation of Cicero's Epistles, but I interrupted it from Sept. 27th to Feb. 8th. I believe it was in this Vacation, or in the October term, that I began every evening to read Thucydides very carefully, as my notes are marked 1822 and 1823. On August 27 I find that I was reading Ovid's Fasti.

"Another subject partly occupied my thoughts, which, though not very wise, yet gave me some Cambridge celebrity. In July 1819 I had sketched a plan for constructing reflecting telescopes with silvered glass, and had shewn it afterwards to Mr Peacock. I now completed the theory of this construction by correcting the aberrations, spherical as well as chromatic. On July 13th, 1822, I drew up a paper about it for Mr Peacock. He approved it much, and in some way communicated it to Mr Herschel. I was soon after introduced to Herschel at a breakfast with Mr Peacock: and he approved of the scheme generally. On August 5th I drew up a complete mathematical paper for the Cambridge Philosophical Society, which I entrusted to Mr Peacock. The aberrations, both spherical and chromatic, are here worked out very well. On Nov. 25th it was read at the meeting of the Philosophical Society, and was afterwards printed in their Transactions: this was my first printed Memoir. Before this time however I had arranged to try the scheme practically. Mr Peacock had engaged to bear the expense, but I had no occasion to ask him. Partly through Drinkwater, I communicated with an optician named Bancks, in the Strand, who constructed the optical part. I subsequently tried my telescope, but it would not do. The fault, as I had not and have not the smallest doubt, depends in some way on the crystallization of the mercury silvering. It must have been about this time that I was introduced to Mr South, at a party at Mr Peacock's rooms. He advised me to write to Tulley, a well-known practical optician, who made me some new reflectors, &c. . However the thing failed practically, and I was too busy ever after to try it again.

"During the October term I had no pupils. I kept my second Act on Nov. 6 , and an Opponency against Jeffries on Nov. 7. I attended the Questionists' Examinations. I seem to have lived a very comfortable idle life. The Commemoration Day was Dec. 18th, when I received a Prize, and the next day I walked to Bury. On Jan. 4th, 1823, I returned to Cambridge, and until the B.A. Examination I read novels and played cards more than at any other time in College.

"On Thursday, Jan. 9th, 1823, the preliminary classes, for arrangement of details of the B.A. Examination, were published. The first class, Airy, Drinkwater, Jeffries, Mason. As far as I remember, the rule was then, that on certain days the classes were grouped thus: 1st, , &c., and on certain other days thus: , , &c. On Saturday, Jan. 11th, I paid fees. On Monday, Jan. 13th, the proceedings of examination began by a breakfast in the Combination Room. After this, Gibson gave me breakfast every day, and Buckle gave me and some others a glass of wine after dinner. The hours were sharp, the season a cold one, and no fire was allowed in the Senate House where the Examination was carried on , and altogether it was a severe time.

"The course of Examination was as follows:

"Monday, Jan. 13th. 8 to 9, printed paper of questions by Mr Hind ; half-past 9 to 11, questions given orally; 1 to 3, ditto; 6 to 9, paper of problems at Mr Higman's rooms.

"Tuesday, Jan. 14th. 8 to 9, Higman's paper; half-past 9 to 11, questions given orally; 1 to 3, ditto; 6 to 9, paper of problems in Sidney College Hall.

"Wednesday, Jan. 15th. Questions given orally 8 to 9 and 1 to 3, with paper of questions on Paley and Locke .

"Thursday, Jan. 16th. We went in at 9 and 1, but there seems to have been little serious examination.

"Friday, Jan. 17. On this day the brackets or classes as resulting from the examination were published, 1st bracket Airy, 2nd bracket Jeffries, 3rd bracket Drinkwater, Fisher, Foley, Mason, Myers.

"On Saturday, Jan. 18th, the degrees were conferred in the usual way. It had been arranged that my brother and sister should come to see me take my degree of B.A., and I had asked Gibson to conduct them to the Senate House Gallery: but Mr Hawkes found them and stationed them at the upper end of the Senate House. After the preliminary arrangements of papers at the Vice-Chancellor's table, I, as Senior Wrangler, was led up first to receive the degree, and rarely has the Senate House rung with such applause as then filled it. For many minutes, after I was brought in front of the Vice-Chancellor, it was impossible to proceed with the ceremony on account of the uproar. I gave notice to the Smith's Prize Electors of my intention to 'sit' for that prize, and dined at Rothman's rooms with Drinkwater, Buckle, and others. On Monday, Jan. 20th, I was examined by Professor Woodhouse, for Smith's Prize, from 10 to 1. I think that the only competitor was Jeffries. On Tuesday I was examined by Prof. Turton, 10 to 1, and on Wednesday by Prof. Lax, 10 to 1. On Thursday, Jan. 23rd, I went to Bury by coach, on one of the coldest evenings that I ever felt.

"Mr Peacock had once recommended me to sit for the Chancellor's medal . But he now seemed to be cool in his advice, and I laid aside all thought of it."

It seems not out of place to insert here a copy of some "Cambridge Reminiscences" written by Airy, which will serve to explain the Acts and Opponencies referred to in the previous narrative, and other matters.

THE ACTS.

The examination for B.A. degrees was preceded, in my time, by keeping two Acts, in the Schools under the University Library: the second of them in the October term immediately before the examination; the first in the October term of the preceding year.

These Acts were reliques of the Disputations of the Middle Ages, which probably held a very important place in the discipline of the University. The presiding authority was one of the Moderators. I apprehend that the word "Moderator" signified "President," in which sense it is still used in the Kirk of Scotland; and that it was peculiarly applied to the Presidency of the Disputations, the most important educational arrangement in the University. The Moderator sent a summons to the "Respondent" to submit three subjects for argument, and to prepare to defend them on a given day: he also named three Opponents. This and all the following proceedings were conducted in Latin. For my Act of 1822, Nov. 6, I submitted the following subjects:

"Recte statuit Newtonus in Principiis suis Mathematicis, libro primo, sectione undecim?."

"Recte statuit Woodius de Iride."

"Recte statuit Paleius de Obligationibus."

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