In the October Term 1819, the only books on Pure Mathematics were:--Euclid generally, Algebra by Dr Wood (formerly Tutor, but in 1819 Master, of St John's College), Vince's Fluxions and Dealtry's Fluxions, Woodhouse's and other Trigonometries. Not a whisper pa.s.sed through the University generally on the subject of Differential Calculus; although some papers (subsequently much valued) on that subject had been written by Mr Woodhouse, fellow of Caius College; but their style was repulsive, and they never took hold of the University. Whewell's Mechanics (1819) contains a few and easy applications of the Differential Calculus. The books on applied Mathematics were Wood's Mechanics, Whewell's Mechanics, Wood's Optics, Vince's Hydrostatics, Vince's Astronomy, Woodhouse's Plane Astronomy (perhaps rather later), The First Book of Newton's Principia: I do not remember any others. These works were undoubtedly able; and for the great proportion of University students going into active life, I do not conceal my opinion that books constructed on the principles of those which I have cited were more useful than those exclusively founded on the more modern system. For those students who aimed at the mastery of results more difficult and (in the intellectual sense) more important, the older books were quite insufficient. More aspiring students read, and generally with much care, several parts of Newton's Principia, Book I., and also Book III. (perhaps the n.o.blest example of geometrical form of cosmical theory that the world has seen). I remember some questions from Book III. proposed in the Senate-House Examination 1823.

In the October term 1819, I went up to the University. The works of Wood and Vince, which I have mentioned, still occupied the lecture-rooms. But a great change was in preparation for the University Course of Mathematics. During the great Continental war, the intercourse between men of science in England and in France had been most insignificant. But in the autumn of 1819, three members of the Senate (John Herschel, George Peac.o.c.k, and Charles Babbage) had entered into the mathematical society of Paris, and brought away some of the works on Pure Mathematics (especially those of Lacroix) and on Mechanics (princ.i.p.ally Poisson's). In 1820 they made a translation of Lacroix's Differential Calculus; and they prepared a volume of Examples of the Differential and Integral Calculus. These were extensively studied: but the form of the College Examinations or the University Examinations was not, I think, influenced by them in the winter 1820-1821 or the two following terms. But in the winter 1821-1822 Peac.o.c.k was one of the Moderators; and in the Senate-House Examination, January 1822, he boldly proposed a Paper of important questions entirely in the Differential Calculus. This was considered as establishing the new system in the University. In January 1823, I think the two systems were mingled. Though I was myself subject to that examination, I grieve to say that I have forgotten much of the details, except that I well remember that some of the questions referred to Newton, Book III. on the Lunar Theory. To these I have already alluded.

No other work occurs to me as worthy of mention, except Woodhouse's Lunar Theory, entirely founded on the Differential Calculus. The style of this book was not attractive, and it was very little read.

CHAPTER III.

AT TRINITY COLLEGE, CAMBRIDGE, FROM HIS TAKING HIS B.A. DEGREE TO HIS TAKING CHARGE OF THE CAMBRIDGE OBSERVATORY AS PLUMIAN PROFESSOR.

FROM JANUARY 18TH, 1823, TO MARCH 15TH, 1828.

"On Jan. 30th, 1823, I returned to Cambridge. I had already heard that I had gained the 1st Smith's Prize, and one of the first notifications to me on my return was that the Walker's good-conduct prize of _10_ was awarded to me.

"I remember that my return was not very pleasant, for our table in hall was half occupied by a set of irregular men who had lost terms and were obliged to reside somewhat longer in order to receive the B.A. degree. But at the time of my completing the B.A. degree (which is not till some weeks after the examination and admission) I with the other complete bachelors was duly invited to the table of the B.A.

scholars, and that annoyance ended.

"The liberation from undergraduate study left me at liberty generally to pursue my own course (except so far as it was influenced by the preparation for fellowship examination), and also left me at liberty to earn more money, in the way usual with the graduates, by taking undergraduate pupils. Mr Peac.o.c.k recommended me to take only four, which occupied me four hours every day, and for each of them I received 20 guineas each term. My first pupils, for the Lent and Easter terms, were Williamson (afterwards Head Master of Westminster School), James Parker (afterwards Q.C. and Vice-Chancellor), Bissett, and Clinton of Caius. To all these I had been engaged before taking my B.A. degree.

"I kept up cla.s.sical subjects. I have a set of notes on the [Greek: Ploutos] and [Greek: Nephelai] of Aristophanes, finished on Mar. 15th, 1823, and I began my daily writing of Latin as usual on Feb. 8th. In mathematics I worked very hard at Lunar and Planetary Theories. I have two MS. books of Lunar Theory to the 5th order of small quant.i.ties, which however answered no purpose except that of making me perfectly familiar with that subject. I worked well, upon my quires, the figure of Saturn supposed h.o.m.ogeneous as affected by the attraction of his ring, and the figure of the Earth as heterogeneous, and the Calculus of Variations. I think it was now that I wrote a MS. on constrained motion.

"On Mar. 17th, 1823, I was elected Fellow of the Cambridge Philosophical Society. On May 9th a cast of my head was taken for Dr Elliotson, an active phrenologist, by Deville, a tradesman in the Strand.

"I had long thought that I should like to visit Scotland, and on my once saying so to my mother, she (who had a most kindly recollection of Alnwick) said in a few words that she thought I could not do better. I had therefore for some time past fully determined that as soon as I had sufficient spare time and money enough I would go to Scotland. The interval between the end of Easter Term and the usual beginning with pupils in the Long Vacation offered sufficient time, and I had now earned a little money, and I therefore determined to go, and invited my sister to accompany me. I had no private introductions, except one from James Parker to Mr Reach, a writer of Inverness: some which Drinkwater sent being too late. On May 20th we went by coach to Stamford; thence by Pontefract and Oulton to York, where I saw the Cathedral, which _then_ disappointed me, but I suppose that we were tired with the night journey. Then by Newcastle to Alnwick, where we stopped for the day to see my birthplace. On May 24th to Edinburgh. On this journey I remember well the stone walls between the fields, the place (in Yorkshire) where for the first time in my life I saw rock, the Hambleton, Kyloe, Cheviot and Pentland Hills, Arthur's Seat, but still more strikingly the revolving Inch Keith Light. At Edinburgh I hired a horse and gig for our journey in Scotland, and we drove by Queensferry to Kinross (where for the first time in my life I saw clouds on the hills, viz. on the Lomond Hills), and so to Perth. Thence by Dunkeld and Killicrankie to Blair Athol (the dreariness of the Drumochter Pa.s.s made a strong impression on me), and by Aviemore (where I saw snow on the mountains) to Inverness. Here we received much kindness and attention from Mr Reach, and after visiting the Falls of Foyers and other sights we went to Fort Augustus and Fort William. We ascended Ben Nevis, on which there was a great deal of snow, and visited the vitrified fort in Glen Nevis. Then by Inverary to Tarbet, and ascended Ben Lomond, from whence we had a magnificent view. We then pa.s.sed by Loch Achray to Glasgow, where we found James Parker's brother (his father, of the house of Macinroy and Parker, being a wealthy merchant of Glasgow). On June 15th to Mr Parker's house at Blochairn, near Glasgow (on this day I heard Dr Chalmers preach), and on the 17th went with the family by steamer (the first that I had seen) to Fairly, near Largs. I returned the gig to Edinburgh, visited Arran and Bute, and we then went by coach to Carlisle, and by Penrith to Keswick (by the old road: never shall I forget the beauty of the approach to Keswick). After visiting Ambleside and Kendal we returned to Cambridge by way of Leeds, and posted to Bury on the 28th June. The expense of this expedition was about _81_. It opened a completely new world to me.

"I had little time to rest at Bury. In the preceding term Drinkwater, Buckle, and myself, had engaged to go somewhere into the country with pupils during the Long Vacation (as was customary with Cambridge men). Buckle however changed his mind. Drinkwater went to look for a place, fixed on Swansea, and engaged a house (called the Cambrian Hotel, kept by a Captain Jenkins). On the morning of July 2nd I left Bury for London and by mail coach to Bristol. On the morning of July 3rd by steamer to Swansea, and arrived late at night. I had then five pupils: Parker, Harman Lewis (afterwards Professor in King's College, London), Pierce Morton, Gibson, and Guest of Caius (afterwards Master of the College). Drinkwater had four, viz. two Malkins (from Bury), Elphinstone (afterwards M.P.), and Farish (son of Professor Farish). We lived a hard-working strange life. My pupils began with me at six in the morning: I was myself reading busily. We lived completely _en famille_, with two men-servants besides the house establishment. One of our first acts was to order a four-oared boat to be built, fitted with a lug-sail: she was called the Granta of Swansea. In the meantime we made sea excursions with boats borrowed from ships in the port. On July 23rd, with a borrowed boat, we went out when the sea was high, but soon found our boat unmanageable, and at last got into a place where the sea was breaking heavily over a shoal, and the two of the crew who were nearest to me (A. Malkin and Lewis), one on each side, were carried out: they were good swimmers and we recovered them, though with some trouble: the breaker had pa.s.sed quite over my head: we gained the sh.o.r.e and the boat was taken home by land. When our own boat was finished, we had some most picturesque adventures at the Mumbles, Aberavon, Caswell Bay, Ilfracombe, and Tenby. From all this I learnt navigation pretty well. The mixture of hard study and open-air exertion seemed to affect the health of several of us (I was one): we were covered with painful boils.

"My Latin-writing began again on July 25th: I have notes on Demosthenes, Lucretius, and Greek History. In mathematics I find Chances, Figure of the Earth with variable density, Differential Equations, Partial Differentials, sketch for an instrument for shewing refraction, and Optical instruments with effects of chromatic aberration. In August there occurred an absurd quarrel between the Fellows of Trinity and the undergraduates, on the occasion of commencing the building of King's Court, when the undergraduates were not invited to wine, and absented themselves from the hall.

"There were vacant this year (1823) five fellowships in Trinity College. In general, the B.A.'s of the first year are not allowed to sit for fellowships: but this year it was thought so probable that permission would be given, that on Sept. 2nd Mr Higman, then appointed as Tutor to a third 'side' of the College, wrote to me to engage me as a.s.sistant Mathematical Tutor in the event of my being elected a Fellow on Oct. 1st, and I provisionally engaged myself. About the same time I had written to Mr Peac.o.c.k, who recommended me to sit, and to Mr Whewell, who after consultation with the Master (Dr Wordsworth), discouraged it. As there was no absolute prohibition, I left Swansea on Sept. 11th (before my engagement to my pupils was quite finished) and returned to Cambridge by Gloucester, Oxford, and London. I gave in my name at the b.u.t.teries as candidate for fellowship, but was informed in a day or two that I should not be allowed to sit. On Sept. 19th I walked to Bury.

"I walked back to Cambridge on Oct. 17th, 1823. During this October term I had four pupils: Neate, Cankrein, Turner (afterwards 2nd wrangler and Treasurer of Guy's Hospital), and William Hervey (son of the Marquis of Bristol). In the Lent term I had four (Neate, Cankrein, Turner, Clinton). In the Easter term I had three (Neate, Cankrein, Turner).

"My daily writing of Latin commenced on Oct. 27th. In November I began re-reading Sophocles with my usual care. In mathematics I find investigations of Motion in a resisting medium, Form of Saturn, Draft of a Paper about an instrument for exhibiting the fundamental law of refraction (read at the Philosophical Society by Mr Peac.o.c.k on Nov. 10th, 1823), Optics, Solid Geometry, Figure of the Earth with variable density, and much about attractions. I also in this term wrote a MS. on the Calculus of Variations, and one on Wood's Algebra, 2nd and 4th parts. I have also notes of the temperature of mines in Cornwall, something on the light of oil-gas, and reminiscences of Swansea in a view of Oswick Bay. In November I attended Professor Sedgwick's geological lectures.

"At some time in this term I had a letter from Mr South (to whom I suppose I had written) regarding the difficulty of my telescope: he was intimately acquainted with Tulley, and I suppose that thus the matter had become more fully known to him. He then enquired if I could visit him in the winter vacation. I accordingly went from Bury, and was received by him at his house in Blackman Street for a week or more with great kindness. He introduced me to Sir Humphrey Davy and many other London savans, and shewed me many London sights and the Greenwich Observatory. I also had a little practice with his own instruments. He was then on intimate terms with Mr Herschel (afterwards Sir John Herschel), then living in London, who came occasionally to observe double stars. This was the first time that I saw practical astronomy. It seems that I borrowed his mountain barometer. In the Lent term I wrote to him regarding the deduction of the parallax of Mars, from a comparison of the relative positions of Mars and 46 Leonis, as observed by him and by Rumker at Paramatta. My working is on loose papers. I see that I have worked out perfectly the interpolations, the effects of uncertainty of longitude, &c., but I do not see whether I have a final result.

"In Jan. 1824, at Playford, I was working on the effects of separating the two lenses of an object-gla.s.s, and on the kind of eye-piece which would be necessary: also on spherical aberrations and Saturn's figure. On my quires at Cambridge I was working on the effects of separating the object-gla.s.s lenses, with the view of correcting the secondary spectrum: and on Jan. 31st I received some numbers (indices of refraction) from Mr Herschel, and reference to Fraunhofer's numbers.

"About this time it was contemplated to add to the Royal Observatory of Greenwich two a.s.sistants of superior education. Whether this scheme was entertained by the Admiralty, the Board of Longitude, or the Royal Society, I do not know. Somehow (I think through Mr Peac.o.c.k) a message from Mr Herschel was conveyed to me, acquainting me of this, and suggesting that I should be an excellent person for the princ.i.p.al place. To procure information, I went to London on Sat.u.r.day, Feb. 7th, sleeping at Mr South's, to be present at one of Sir Humphrey Davy's Sat.u.r.day evening soirees (they were then held every Sat.u.r.day), and to enquire of Sir H. Davy and Dr Young. When I found that succession to the post of Astronomer Royal was not considered as distinctly a consequence of it, I took it coolly, and returned the next night. The whole proposal came to nothing.

"At this time I was engaged upon differential equations, mountain barometer problem and determination of the height of the Gogmagogs and several other points, investigations connected with Laplace's calculus, spherical aberration in different planes, geology (especially regarding Derbyshire, which I proposed to visit), and much of optics. I wrote a draft of my Paper on the figure of Saturn, and on Mar. 15th, 1824, it was read at the Philosophical Society under the t.i.tle of 'On the figure a.s.sumed by a fluid h.o.m.ogeneous ma.s.s, whose particles are acted on by their mutual attraction, and by small extraneous forces,' and is printed in their Memoirs. I also wrote a draft of my Paper on Achromatic Eye-pieces, and on May 17th, 1824, it was read at the Philosophical Society under the t.i.tle of 'On the Principles and Construction of the Achromatic Eye-pieces of Telescopes, and on the Achromatism of Microscopes,' including also the effects of separating the lenses of the object-gla.s.s. It is printed in their Memoirs.

"Amongst miscellaneous matters I find that on Mar. 22nd of this year I began regularly making extracts from the books of the Book Society, a practice which I continued to March 1826. On Mar. 27th, a very rainy day, I walked to Bury to attend the funeral of my uncle William Biddell, near Diss, and on Mar. 30th I walked back in rain and snow. On Feb. 24th I dined with Cubitt in Cambridge. On May 21st I gave a certificate to Rogers (the a.s.sistant in Crosse's school, and my instructor in mathematics), which my mother amplified much, and which I believe procured his election as master of Walsall School. On June 23rd I went to Bury. The speeches at Bury School, which I wished to attend, took place next day."

At this point of his Autobiography the writer continues, "Now came one of the most important occurrences in my life." The important event in question was his acquaintance with Richarda Smith, the lady who afterwards became his wife. The courtship was a long one, and in the Autobiography there are various pa.s.sages relating to it, all written in the most natural and unaffected manner, but of somewhat too private a nature for publication. It will therefore be convenient to digress from the straight path of the narrative in order to insert a short memoir of the lady who was destined to influence his life and happiness in a most important degree.

Richarda Smith was the eldest daughter of the Rev. Richard Smith, who had been a Fellow of Trinity College, Cambridge, but was at this time Private Chaplain to the Duke of Devonshire, and held the small living of Edensor, near Chatsworth, in Derbyshire. He had a family of two sons and seven daughters, whom he had brought up and educated very carefully. Several of his daughters were remarkable both for their beauty and accomplishments. Richarda Smith was now in her 20th year, and the writer of the Autobiography records that "at Matlock we received great attention from Mr Chenery: in speaking of Mr Smith I remember his saying that Mr Smith had a daughter whom the Duke of Devonshire declared to be the most beautiful girl he ever saw." This was before he had made the acquaintance of the family. Airy was at this time on a walking tour in Derbyshire with his brother William, and they were received at Edensor by Mr Smith, to whom he had letters of introduction. He seems to have fallen in love with Miss Smith "at first sight," and within two days of first seeing her he made her an offer of marriage. Neither his means nor his prospects at that time permitted the least idea of an immediate marriage, and Mr Smith would not hear of any engagement. But he never had the least doubt as to the wisdom of the choice that he had made: he worked steadily on, winning fame and position, and recommending his suit from time to time to Miss Smith as opportunity offered, and finally married her, nearly six years after his first proposal. His constancy had its reward, for he gained a most charming and affectionate wife. As he records at the time of his marriage, "My wife was aged between 25 and 26, but she scarcely appeared more than 18 or 20. Her beauty and accomplishments, her skill and fidelity in sketching, and above all her exquisite singing of ballads, made a great sensation in Cambridge."

Their married life lasted 45 years, but the last six years were saddened by the partial paralysis and serious illness of Lady Airy. The entire correspondence between them was most carefully preserved, and is a record of a most happy union. The letters were written during his numerous journeys and excursions on business or pleasure, and it is evident that his thoughts were with her from the moment of their parting. Every opportunity of writing was seized with an energy and avidity that shewed how much his heart was in the correspondence. Nothing was too trivial or too important to communicate to his wife, whether relating to family or business matters. The letters on both sides are always full of affection and sympathy, and are written in that spirit of confidence which arises from a deep sense of the value and necessity of mutual support in the troubles of life. And with his active and varied employments and his numerous family there was no lack of troubles. They were both of them simple-minded, sensible, and practical people, and were very grateful for such comforts and advantages as they were able to command, but for nothing in comparison with their deep respect and affection for one another.

Both by natural ability and education she was well qualified to enter into the pursuits of her husband, and in many cases to a.s.sist him. She always welcomed her husband's friends, and by her skill and attractive courtesy kept them well together. She was an admirable letter-writer, and in the midst of her numerous domestic distractions always found time for the duties of correspondence. In conversation she was very attractive, not so much from the wit or brilliancy of her remarks as from the brightness and interest with which she entered into the topics under discussion, and from the unfailing grace and courtesy with which she attended to the views of others. This was especially recognized by the foreign astronomers and men of science who from time to time stayed as guests at the Observatory and to whom she acted as hostess. Although she was not an accomplished linguist yet she was well able to express herself in French and German, and her natural good sense and kindliness placed her guests at their ease, and made them feel themselves (as indeed they were) welcomed and at home.

Her father, the Rev. Richard Smith, was a man of most cultivated mind, and of the highest principles, with a keen enjoyment of good society, which the confidence and friendship of his patron the Duke of Devonshire amply secured to him, both at Chatsworth and in London. He had a deep attachment to his Alma Mater of Cambridge, and though not himself a mathematician he had a great respect for the science of mathematics and for eminent mathematicians. During the long courtship already related Mr Smith conceived the highest respect for Airy's character, as well as for his great repute and attainments, and expressed his lively satisfaction at his daughter's marriage. Thus on January 20th, 1830, he wrote to his intended son-in-law as follows: "I have little else to say to you than that I continue with heartfelt satisfaction to reflect on the important change about to take place in my dear daughter's situation. A father must not allow himself to dilate on such a subject: of course I feel confident that you will have no reason to repent the irrevocable step you have taken, but from the manner in which Richarda has been brought up, you will find such a helpmate in her as a man of sense and affection would wish to have, and that she is well prepared to meet the duties and trials (for such must be met with) of domestic life with a firm and cultivated mind, and the warm feelings of a kind heart. Her habits are such as by no means to lead her to expensive wishes, nor will you I trust ever find it necessary to neglect those studies and pursuits upon which your reputation and subsistence are chiefly founded, to seek for idle amus.e.m.e.nts for your companion. I must indulge no further in speaking of her, and have only at present to add that I commit in full confidence into your hands the guardianship of my daughter's happiness." And on April 5th, 1830, shortly after their marriage, he wrote to his daughter thus: "If thinking of you could supply your place amongst us you would have been with us unceasingly, for we have all of us made you the princ.i.p.al object of our thoughts and our talk since you left us, and I travelled with you all your journey to your present delightful home. We had all but one feeling of the purest pleasure in the prospect of the true domestic comfort to which we fully believe you to be now gone, and we rejoice that all your endearing qualities will now be employed to promote the happiness of one whom we think so worthy of them as your dear husband, who has left us in the best opinion of his good heart, as well as his enlightened and sound understanding. His late stay with us has endeared him to us all. Never did man enter into the married state from more honourable motives, or from a heart more truly seeking the genuine happiness of that state than Mr Airy, and he will, I trust, find his reward in you from all that a good wife can render to the best of husbands, and his happiness be reflected on yourself." It would be difficult to find letters of more genuine feeling and satisfaction, or more eloquently expressed, than these.

The narrative of the Autobiography will now be resumed.

"I had been disappointed two years before of an expedition to Derbyshire. I had wished still to make it, and my brother wished to go: and we determined to make it this year (1824). We were prepared with walking dresses and knapsacks. I had well considered every detail of our route, and was well provided with letters of introduction, including one to the Rev. R. Smith of Edensor. On June 29th we started by coach to Newmarket and walked through the Fens by Ramsay to Peterborough. Then by Stamford and Ketton quarries to Leicester and Derby. Here we were recognized by a Mr Calvert, who had seen me take my degree, and he invited us to breakfast, and employed himself in shewing us several manufactories, &c. to which we had been denied access when presenting ourselves unsupported. We then went to Belper with an introduction from Mr Calvert to Jedediah Strutt: saw the great cotton mills, and in the evening walked to Matlock. Up to this time the country of greatest interest was the region of the fens about Ramsay (a most remarkable district), but now began beauty of scenery.

On July 9th we walked by Rowsley and Haddon Hall over the hills to Edensor, where we stayed till the 12th with Mr Smith. We next visited Hathersage, Castleton, and Marple (where I wished to see the ca.n.a.l aqueduct), and went by coach to Manchester, and afterwards to Liverpool. Here Dr Traill recommended us to see the Pontycyssylte Aqueduct, and we went by Chester and Wrexham to Rhuabon, saw the magnificent work, and proceeded to Llangollen. Thence by Chester and Northwich (where we descended a salt-mine) to Macclesfield. Then to the Ecton mine (of which we saw but little) through Dovedale to Ashbourn, and by coach to Derby. On July 24th to Birmingham, where we found Mr Guest, lodged in his house, and were joined by my pupil Guest. Here we were fully employed in visiting the manufactures, and then went into the iron country, where I descended a pit in the Staffordshire Main. Thence by coach to Cambridge, where I stopped to prepare for the Fellowship Examination.

"I had two pupils in this portion of the Long Vacation, Turner and Dobbs. On August 2nd my writing of Latin began regularly as before. My princ.i.p.al mathematics on the quires are Optics. On August 25th I made experiments on my left eye, with good measures, and on Aug. 26th ordered a cylindrical lens of Peters, a silversmith in the town, which I believe was never made. Subsequently, while at Playford, I ordered cylindrical lenses of an artist named Fuller, living at Ipswich, and these were completed in November, 1824.

"My letter to the Examiners, announcing my intention of sitting for Fellowship (which like all other such doc.u.ments is preserved on my quires) was delivered on Sept 21st. The Examination took place on Sept. 22nd and the two following days. On Oct. 1st, 1824, at the usual hour of the morning, I was elected Fellow. There were elected at the same time T.B. Macaulay (afterwards Lord Macaulay), who was a year senior to me in College, and I think Field of my own year. I drew up my letter of acknowledgment to the Electors. On Oct. 2nd at 9 in the morning I was admitted Fellow with the usual ceremonies, and at 10 I called on the Electors with my letter of acknowledgment. I immediately journeyed to Derbyshire, paid a visit at Edensor, and returned by Sheffield.

"On Oct. 11th (it having been understood with Mr Higman that my engagement as a.s.sistant Mathematical Tutor stood) the Master sent for me to appoint me and to say what was expected as duty of the office. He held out to me the prospect of ultimately succeeding to the Tutorship, and I told him that I hoped to be out of College before that time.

"About this time the 'Athenaeum,' a club of a scientific character, was established in London, and I was nominated on it, but I declined"

(Oct. 14th). In this year (1824) I commenced account with a banker by placing _110_ in the hands of Messrs Mortlock and Co. On Oct. 16th I walked to Bury, and after a single day's stay there returned to Cambridge.

"On Oct. 23rd, 1824,1 began my lectures as Mathematical a.s.sistant Tutor. I lectured the Senior Sophs and Junior Sophs on Higman's side. The number of Senior Sophs was 21. Besides this I took part in the 'Examinations of the Questionists,' a series of exercises for those who were to take the Bachelor's degree in the next January. I examined in Mechanics, Newton, and Optics. I had also as private pupils Turner, Dobbs, and Cooper. I now ceased from the exercise which I had followed with such regularity for five years, namely that of daily writing Latin. In its stead I engaged a French Master (Goussel) with whom I studied French with reasonable a.s.siduity for the three terms to June, 1825.

"Among mathematical investigations I find: Theory of the Moon's brightness, Motion of a body in an ellipse round two centres of force, Various differential equations, Numerical computation of sin pi from series, Numerical computation of sines of various arcs to 18 decimals, Curvature of surfaces in various directions, Generating functions, Problem of sound. I began in the winter a Latin Essay as competing for the Middle Bachelors' Prize, but did not proceed with it. I afterwards wished that I had followed it up: but my time was fully occupied.

"On Jan. 28th, 1825, I started for Edensor, where I paid a visit, and returned on Feb. 2nd. On Feb. 4th I wrote to Mr Clarkson, asking his advice about a profession or mode of life (the cares of life were now beginning to press me heavily, and continued to do so for several years). He replied very kindly, but his answer amounted to nothing.

About the same time I had some conversation of the same kind with Mr Peac.o.c.k, which was equally fruitless.

"On Feb. 4th I have investigations of the density of light near a caustic (on the theory of emissions). On Feb. 5th I finished a Paper about the defect in my eye, which was communicated to the Cambridge Philosophical Society on Feb. 21st. Mr Peac.o.c.k or Mr Whewell had some time previously applied to me to write a Paper on Trigonometry for the Encyclopaedia Metropolitana, and I had been collecting some materials (especially in regard to its history) at every visit to London, where I read sometimes at the British Museum: also in the Cambridge libraries. I began this Paper (roughly) on Feb. 8th, and finished it on Mar. 3rd. The history of which I speak, by some odd management of the Editors of the Encyclopaedia, was never published. The MS. is now amongst the MSS. of the Royal Observatory, Greenwich. Other subjects on my quires are: Theory of musical concords, many things relating to trigonometry and trigonometrical tables, achromatic eye-pieces, equation to the surface bounding the rays that enter my left eye, experiments on percussion. Also notes on c.u.mberland and Wales (I had already proposed to myself to take a party of pupils in the Long Vacation to Keswick), and notes on history and geology.

"I had been in correspondence with Dr Malkin (master of Bury School), who on Feb. 8th sent a certificate for my brother William, whom I entered at Trinity on Peac.o.c.k's side. On Mar. 25th I changed my rooms, quitting those on the ground-floor east side of Queen Mary's Gate for first-floor rooms in Neville's Court, south side, the easternmost rooms. In this term my lectures lasted from Apr. 18th to May 14th. Apparently I had only the Senior Sophs, 19 in number, and the same four pupils (Turner, Dobbs, Cooper, Hovenden) as in the preceding term. The only scientific subjects on which I find notes are, a Paper on the forms of the Teeth of Wheels, communicated to the Philosophical Society on May 2nd; some notes about Musical Concords, and some examination of a strange piece of Iceland Spar. On Apr. 29th I was elected to the Northern Inst.i.tution (of Inverness); the first compliment that I received from an extraneous body.

"On May 14th I have a most careful examination of my money accounts, to see whether I can make an expedition with my sister into Wales. My sister came to Cambridge, and on Monday, May 23rd, 1825, we started for Wales, equipped in the lightest way for a walking expedition. We went by Birmingham to Shrewsbury: then to the Pontycyssylte Aqueduct and by various places to Bala, and thence by Llanrwst to Conway. Here the suspension bridge was under construction: the mole was made and the piers, but nothing else. Then on to Bangor, where nine chains of the suspension bridge were in place, and so to Holyhead. Then by Carnarvon to Bethgelert, ascending Snowdon by the way, and in succession by Festiniog, Dolgelly, and Aberystwyth to Hereford (the first time that I had visited it since my father left it). From thence we went by coach to London, and I went on to Cambridge on the 23rd of June.

"I had arranged to take a party of pupils to Keswick, and to take my brother there. Mr Clarkson had provided me with introductions to Mr Southey and Mr Wordsworth. On Wednesday, June 29th, 1825, we started, and went by Leicester, Sheffield, Leeds, and Kendal, to Keswick, calling at Edensor on the way. My pupils were Cleasby, Marshman, Clinton, Wigram, Tottenham, and M. Smith. At Keswick I pa.s.sed three months very happily. I saw Mr Southey's family frequently, and Mr Wordsworth's occasionally. By continual excursions in the neighbourhood, and by a few excursions to places as distant as Bowness, Calder Bridge, &c. (always climbing the intermediate mountains), I became well acquainted with almost the whole of that beautiful country, excepting some of the S. W. dales. A geological hammer and a mountain barometer were very interesting companions. I had plenty of work with my pupils: I worked a little Lunar Theory, a little of Laplace's Equations, something of the Figure of the Earth, and I wrote out very carefully my Trigonometry for the Encyclopaedia Metropolitana. I read a little of Machiavelli, and various books which I borrowed of Mr Southey. On Friday, Sept. 30th, my brother and I left for Kendal, and after a stay of a few days at Edensor, arrived at Cambridge on Oct. 11th.

"On Oct. 21st my Lectures to the Junior Sophs began, 39 names, lasting to Dec. 13th. Those to the Senior Sophs, 16 names, Oct 29th to Dec. 10th. I also examined Questionists as last year. I have notes about a Paper on the connection of impact and pressure, read at the Philosophical Society on Nov. 14th, but not printed, dipping-needle problems, curve described round three centres of force, barometer observations, theory of the Figure of the Earth with variable density, and effect on the Moon, correction to the Madras pendulum, wedge with friction, spots seen in my eyes, density of rays near a caustic. In this term I accomplished the preparation of a volume of Mathematical Tracts on subjects which, either from their absolute deficiency in the University or from the unreadable form in which they had been presented, appeared to be wanted. The subjects of my Tracts were, Lunar Theory (begun Oct. 26th, finished Nov. 1st), Figure of the Earth (1st part finished Nov. 18th), Precession and Nutation (my old MS. put in order), and the Calculus of Variations. I applied, as is frequently done, to the Syndicate of the University Press for a.s.sistance in publishing the work; and they agreed to give me paper and printing for 500 copies. This notice was received from Professor Turton on Nov. 29th, 1825. It was probably also in this year that I drew up an imperfect 'Review' of Coddington's Optics, a work which deserved severe censure: my review was never finished.

"In the Long Vacation at Keswick I had six pupils at _42_ each. In the October term I had Marshman and Ogilby at _105_ for three terms, and Dobbs at _75_ for three terms. I had, at Mr Peac.o.c.k's suggestion, raised my rate from 60 to 100 guineas for three terms: this prevented some from applying to me, and induced some to withdraw who had been connected with me: but it did me no real hurt, for engrossment by pupils is the worst of all things that can happen to a man who hopes to distinguish himself. On Dec. 17th I went to Bury, and returned to Cambridge on Jan. 30th, 1826.

"I have the attendance-bills of my Lectures to Senior Sophs (16) from Feb. 3rd to Feb. 23rd, and to Freshmen (40) from Feb. 27th to Mar. 15. It would appear that I gave but one college-lecture per day (my belief was that I always had two). The tutor's stipend per term was _50_. On my quires I find, Investigations for the ellipticity of a heterogeneous spheroid when the density is expressed by sin _qc_/_qc_ (the remarkable properties of which I believe I discovered entirely myself, although they had been discovered by other persons), Theoretical Numbers for precession, nutation, &c., some investigations using Laplace's Y, hard work on the Figure of the Earth to the 2nd order,'Woodhouse's remaining apparatus,' Notes about Lambton's and Kater's errors, Depolarization, Notes of Papers on depolarization in the Phil. Trans., Magnetic Investigations for Lieut. Foster, Isochronous Oscillations in a resisting medium, Observations on a strange piece of Iceland Spar. On Mar. 7th forwarded Preface and t.i.tle Page for my Mathematical Tracts.

"Some time in this term I began to think of the possibility of observing the diminution of gravity in a deep mine, and communicated with Whewell, who was disposed to join in experiments. My first notion was simply to try the rate of a clock, and the Ecton mine was first thought of. I made enquiries about the Ecton mine through Mr Smith (of Edensor), and visited the mine, but in the meantime Whewell had made enquiries in London and found (princ.i.p.ally from Dr Paris) that the mine of Dolcoath near Camborne in Cornwall would be a better place for the experiment. Dr Paris wrote to me repeatedly, and ultimately we resolved on trying it there. In my papers on Mar. 21st are various investigations about attractions in both mines. On Apr. 3rd I went to London, princ.i.p.ally to arrange about Dolcoath, and during April and May I was engaged in correspondence with Sir H. Davy (President of the Royal Society), Mr Herschel, and Dr Young (Secretary of the Board of Longitude) about the loan of instruments and pendulums. On Apr. 23rd I was practising pendulum-observations (by coincidence); and about this time repeatedly practised transits with a small instrument lent by Mr Sheepshanks (with whom my acquaintance must have begun no long time before) which was erected under a tent in the Fellows'

Walks. On my quires I find various schemes for graduating thermometers for pendulum experiments.

"I find also Notes of examination of my brother William, who had come to College last October; and a great deal of correspondence with my mother and sister and Mr Case, a lawyer, about a troublesome business with Mr Cropley, an old friend of G. Biddell, to whom my father had lent _500_ and whose affairs were in Chancery.

"My lectures in this term were to the Junior Sophs from Apr. 10th to May 13th: they were six in number and not very regular. On Apr. 28th I sent to Mawman the copy of my Trigonometry for the Encyclopaedia Metropolitana, for which I received _42_. I received notice from the Press Syndicate that the price of my Mathematical Tracts was fixed at _6s. 6d._: I sold the edition to Deighton for _70_, and it was immediately published. About this time I have letters from Mr Herschel and Sir H. Davy about a Paper to be presented to the Royal Society--I suppose about the Figure of the Earth to the 2nd order of ellipticity, which was read to the Royal Society on June 15th.