CHAPTER III
UNIVERSITY OF CAMBRIDGE. SCIENTIFIC WORK AS UNDERGRADUATE
Thomson entered at St. Peter's College, Cambridge, in October 1841, and began the course of study then in vogue for mathematical honours. At that time, as always down almost to the present day, everything depended on the choice of a private tutor or "coach," and the devotion of the pupil to his directions, and on adherence to the subjects of the programme. His private tutor was William Hopkins, "best of all private tutors," one of the most eminent of his pupils called him, a man of great attainment and of distinction as an original investigator in a subject which had always deeply interested Thomson—the internal rigidity of the earth. But the curriculum for the tripos did not exhaust Thomson's energy, nor was it possible to keep him entirely to the groove of mastering and writing out book-work, and to the solution of problems of the kind dear to the heart of the mathematical examiner. He wrote original articles for the Cambridge Mathematical Journal, on points in pure and in applied mathematics, and read mathematical books altogether outside the scope of the tripos. Nor did he neglect athletic exercises and amusements; he won the Colquhoun Sculls as an oarsman, and was an active member, and later, during his residence at Cambridge, president of the C.U.M.S., the Cambridge University Musical Society.[6] The musical instruments he favoured were the cornet and especially the French horn—he was second horn in the original Peterhouse band—but nothing seems to be on record as to the difficulties or incidents of his practice! Long afterwards, in a few extremely interesting lectures which he gave annually on sound, he discoursed on the vibrations of columns of air in wind instruments, and sometimes illustrated his remarks by showing how notes were varied in pitch on the old-fashioned French horn, played with the hand in the bell, a performance which always intensely delighted the Natural Philosophy Class.
At the Jubilee commemoration of the society, 1893, Lord Kelvin recalled that Mendelssohn, Weber and Beethoven were the "gods" of the infant association. Those of his pupils who came more intimately in contact with him will remember his keen admiration for these and other great composers, especially Bach, Mozart, and Beethoven, and his delight in hearing their works. The Waldstein sonata was a special favourite. It has been remarked before now, and it seems to be true, that the music of Bach and Beethoven has had special attractions for many great mathematicians.
At Cambridge Thomson made the acquaintance of George Gabriel Stokes, who graduated as Senior Wrangler and First Smith's Prizeman in 1841, and eight years later became Lucasian Professor of Mathematics in the University of Cambridge. Their acquaintance soon ripened into a close friendship, which lasted until the death of Stokes in 1903. The Senior Wrangler and the Peterhouse Undergraduate undertook the composition of a series of notes and papers on points in pure and physical mathematics which required clearing up, or putting in a new point of view; and so began a life-long intercourse and correspondence which was of great value to science.
Thomson's papers of this period are on a considerable variety of subjects, including his favourite subject of the flux of heat. There are sixteen in all that seem to have been written and published during his undergraduate residence at Cambridge. Most of them appeared in the Cambridge Mathematical Journal between 1842 and 1845; but three appeared in 1845 in Liouville's Journal de Mathématiques. Four are on subjects of pure mathematics, such as Dupin's theorem regarding lines of curvature of orthogonally intersecting surfaces, the reduction of the general equation of surfaces of the second order (now called second degree), six are on various subjects of the theory of heat, one is on attractions, five are on electrical theory, and one is on the law of gravity at the surface of a revolving homogeneous fluid. It is impossible to give an account of all these papers here. Some of them are new presentations or new proofs of known theorems, one or two are fresh and clear statements of fundamental principles to be used later as the foundation of more complete statements of mathematical theory; but all are marked by clearness and vigour of treatment.
Another paper, published in the form of a letter, of date October 8, 1845, to M. Liouville, and published in the Journal de Mathématiques in the same year, indicates that either before or shortly after taking his degree, Thomson had invented his celebrated method of "Electric Images" for the solution of problems of electric distribution. Of this method, which is one of the most elegant in the whole range of physical mathematics, and solves at a stroke some problems, otherwise almost intractable, we shall give some account in the following chapter.
This record of work is prodigious for a student reading for the mathematical tripos; and it is somewhat of an irony of fate that such scientific activity is, on the whole, rather a hindrance than a help in the preparation for that elaborate ordeal of examination. Great expectations had been formed regarding Thomson's performance; hardly ever before had a candidate appeared who had done so much and so brilliant original work, and there was little doubt that he would be easily first in any contest involving real mathematical power, that is, ability to deal with new problems and to express new relations of facts in mathematical language. But the tripos was not a test of power merely; it was a test also of acquisition, and, to candidates fairly equal in this respect, also of memory and of quickness of reproduction on paper of acquired knowledge.