In the summer of 1840, he accompanied his father and his brother on a tour through Germany, partly to see the country and partly also, to acquire a practical knowledge of the language. In both these objects, he was somewhat hindered by his fondness for mathematical studies, which led him to include in his impedimenta for the trip a copy of Fourier's _Théorie analytique de la Chaleur_. Most students out on a summer's vacation, especially in foreign parts, would doubtless have preferred to give their minds rest and congenial distraction rather than keep on reading and pondering over abstract mathematical concepts. Our young tourist, on the other hand, seems to have thought of little else than of Fourier's "mathematical poem," as Clerk Maxwell called the work, a "poem" that continued to have a charm for him all through life. It is a noteworthy fact that Thomson continually returned to the ideas and methods of this suggestive treatise on the flow of heat, and that he applied them with great success to problems in thermal conductivity, in electricity and in submarine telegraphy. Shortly after returning home, Thomson was sent to the University of Cambridge, where he entered St. Peter's College, commonly called Peterhouse, one of the oldest colleges of the university, its foundation dating back to the year 1284. Though he, no doubt, followed in a general way the directions given him by William Hopkins, "the best of private tutors," and kept in view the requirements of the honors examination, called the "Mathematical Tripos," for which he intended to present himself at the end of his course, he found his studies somewhat routinal and uninspiring. Original work was more to his taste than conventional subjects; his tutor, however, thought mainly of placing this brilliant pupil at the head of the wranglers, and hailing him the senior wrangler of the year, for which purpose, the beaten track must be followed, the standard works read, favorite problems worked out, short-cuts conned and rapidity of output exercised. Stokes, of Pembroke, had been senior wrangler in 1841; Cayley, of Trinity, in 1842; and Adams, of John's, in 1843; why not Thomson, of Peterhouse, in 1845, argued Hopkins, who had the distinction of being second wrangler of the previous year? But when the ordeal was over and the work of all candidates appraised, Thomson's name was second on the list, with Parkinson, of John's, at the top. Hopkins was disappointed, as he had a right to be, for it was thought by many and said by some that Parkinson was not fit to sharpen Thomson's pencils. At the examination for the Smith's prizes, which immediately followed, and which was generally regarded as a higher honor and a better test of original ability, the order was reversed, and Thomson's star blazed out with the brilliancy of the first magnitude.