The Tripos Examination was held in the early part of January. On the 25th of that month Thomson met his private tutor Hopkins in the "Senior Wranglers' Walk" at Cambridge, and in the course of conversation referred to his desire to obtain a copy of Green's 'Essay' (supra, p. 21). Hopkins at once took him to the rooms where he had attended almost daily for a considerable time as a pupil, and produced no less than three copies of the Essay, and gave him one of them. A hasty perusal showed Thomson that all the general theorems of attractions contained in his paper "On the Uniform Motion of Heat," etc., as well as those of Gauss and Chasles, had been set forth by Green and were derivable from a general theorem of analysis whereby a certain integral taken throughout a space bounded by surfaces fulfilling a certain condition is expressed as two integrals, one taken throughout the space, the other taken over the bounding surface or surfaces. It has been stated in the last chapter that Thomson had established, as a deduction from the flow of heat in a uniform solid from sources distributed within it, the remarkable theorem of the replacement, without alteration of the external flow, of these sources by a certain distribution over any surface of uniform temperature, and had pointed out the analogue of this theorem in electricity. This method of proof was perfectly original and had not been anticipated, though the theorem, as has been stated, had already been given by Green and by Gauss. In the paper entitled "Propositions in the Theory of Attraction," published in the _Cambridge Mathematical Journal_ in November 1842, Thomson gave an analytical proof of this great theorem, but afterwards found that this had been done almost contemporaneously by Sturm in Liouville's Journal. Soon after the Tripos and Smith's Prize Examinations were over, Thomson went to London, and visited Faraday in his laboratory in the Royal Institution. Then he went on to Paris with his friend Hugh Blackburn, and spent the summer working in Regnault's famous laboratory, making the acquaintance of Liouville, Sturm, Chasles, and other French mathematicians of the time, and attending meetings of the Académie des Sciences. He made known to the mathematicians of Paris Green's 'Essay,' and the treasures it contained, and frequently told in after years with what astonishment its results were received. He used to relate that one day, while he and Blackburn sat in their rooms, they heard some one come panting up the stair. Sturm burst in upon them in great excitement, and exclaimed, "_Vous avez un Mèmoire de Green! M. Liouville me l'a dit._" He sat down and turned over the pages of the 'Essay,' looking at one result after another, until he came to a complete anticipation of his proof of the replacement theorem. He jumped up, pointed to the page, and cried out, "_Voila mon affaire!_"