In that period Fourier wrote his memoirs on the conduction of heat, and gave to the world his immortal book to be an inspiration to the physical philosophers of succeeding generations. Legendre had written memoirs which were to lead, in the hands of Jacobi and his successors, to a new province of mathematics, while, in Germany, Gauss had begun his stately march of discovery.

The methods and results of this period of mathematical activity were at first hardly known in this country: the slavish devotion of Cambridge to the geometrical processes and the fluxional notation of Newton, an exclusive partiality which Newton himself would have been the first to condemn, led analytical methods, equally Newtonian, to be stigmatised as innovations, because clothed in the unfamiliar garb of the continental notation. A revolt against this was led by Sir John Herschel, Woodhouse, Peacock, and some others at Cambridge, who wrote books which had a great effect in bringing about a change of methods. Sir John thus described the effect of the new movements:—"Students at our universities, fettered by no prejudices, entangled by no habits, and excited by the ardour and emulation of youth, had heard of the existence of masses of knowledge from which they were debarred by the mere accident of position. They required no more. The prestige which magnifies what is unknown, and the attractions inherent in what is forbidden, coincided in their impulse. The books were procured and read, and produced their natural effects. The brows of many a Cambridge examiner were elevated, half in ire, half in admiration, at the unusual answers which began to appear in examination papers. Even moderators are not made of impenetrable stuff, though fenced with sevenfold Jacquier, and tough bull-hide of Vince and Wood."

The memoirs and treatises of the continental analysts were eagerly procured and studied by James Thomson, and as he was bound by no examination traditions, he freely adopted their methods, so far as these came within the scope of his teaching, and made them known to the English reading public in his text-books. Hence when the chair of Mathematics at Glasgow became vacant in 1832 by the death of Mr. James Millar, Mr. Thomson was at once chosen by the Faculty, which at that time was the electing body.

The Faculty consisted of the Principal and the Professors of Divinity, Church History, Oriental Languages, Natural Philosophy, Moral Philosophy, Mathematics, Logic, Greek, Humanity, Civil Law, Practice of Medicine, Anatomy, and Practical Astronomy. It administered the whole revenues and property of the College, and possessed the patronage of the above-named chairs with the exception of Church History, Civil Law, Medicine, Anatomy, and Astronomy, so that Mr. Thomson became not only Professor of Mathematics, but also, in virtue of his office, a member of what was really the supreme governing body of the University. The members of the Faculty, with the exception of the Professor of Astronomy, who resided at the observatory, were provided with official residences in the College. This arrangement is still adhered to; though now the government is in the hands of a University Court, with the Senate (which formerly only met to confer degrees or to manage the library and some other matters) to regulate and superintend teaching and discipline.

Professor Thomson was by no means the first or the only professor of the name in the University of Glasgow, as the following passage quoted from a letter of John Nichol, son of Dr. J. P. Nichol, and first Professor of English at Glasgow, amusingly testifies:—

"Niebuhr, after examining a portion of the Fasti Consulares, arrived at the conclusion that the senatus populusque Romanus had made a compact to elect every year a member of the Fabian house to one of the highest offices of state, so thickly are the records studded with the name of the Fabii. Some future Niebuhr of the New Zealand Macaulay imagines, turning his attention to the annals of Glasgow College, will undoubtedly arrive at the conclusion that the leaders of that illustrious corporation had, during the period of which I am writing, become bound in a similar manner to the name of Thomson. Members of that great gens filled one-half of the chairs in the University. I will not venture to say how many I have known. There was Tommy Thomson the chemist; William Thomson of Materia Medica; Allen Thomson of Anatomy, brother of the last; Dr. James Thomson of Mathematics; William, his son, etc., etc. Old Dr. James was one of the best of Irishmen, a good mathematician, an enthusiastic and successful teacher, the author of several valuable school-books, a friend of my father's, and himself the father of a large family, the members of which have been prosperous in the world. They lived near us in the court, and we made a pretty close acquaintanceship with them all."

A former Professor of Natural Philosophy, Dr. Anderson,[2] who appears to have lived the closing years of his life in almost constant warfare with his colleagues of the Faculty, and who established science classes for workmen in Glasgow, bequeathed a sum of money to set up a college in Glasgow in which such classes might be carried on. The result was the foundation of what used to be called the "Andersonian University" in George Street, the precursor of the magnificent Technical College of the present day. This name, and the large number of Thomsons who had been and were still connected with the University of Glasgow, caused the more ancient institution to be not infrequently referred to as the "Thomsonian University"!

The Thomas Thomson (no relative of the Belfast Thomsons) affectionately, if a little irreverently, mentioned in the above quotation, was then the Professor of Chemistry. He was the first to establish a chemical laboratory for students in this country; indeed, his laboratory preceded that of Liebig at Giessen by some years, and it is probable that as regards experimental chemistry Glasgow was then in advance of the rest of the world. His pupil and life-long admirer was destined to establish the first physical laboratory for such students as were willing to spend some time in the experimental investigation and verification of physical principles, or to help the professor in his researches. The systematic instruction of students in methods of experimenting by practical exercises with apparatus was a much later idea, and this fact must be taken account of when the laboratories of the present time are contrasted with the much more meagre provision of those early days. The laboratory is now, as much as the lecture-room, the place where classes are held and instruction given in experimental science to crowds of students, and it is a change for the better.

The arrival of James Thomson and his family at Glasgow College, in 1832, was remarked at the time as an event which brought a large reinforcement to the gens already inseparably associated with the place: how great were to be its consequences not merely to the University but to the world at large nobody can then have imagined. His family consisted of four sons and two daughters: his wife, Margaret Gardner, daughter of William Gardner, a merchant in Glasgow, had died shortly before, and the care of the family was undertaken by her sister, Mrs. Gall. The eldest son, James Thomson, long after to be Rankine's successor in the Chair of Engineering, was ten years of age and even then an inveterate inventor; William, the future Lord Kelvin (born June 26, 1824), was a child of eight. Two younger sons were John (born in 1826)—who achieved distinction in Medicine, became Resident Assistant in the Glasgow Royal Infirmary, and died there of a fever caught in the discharge of his duty—and Robert, who was born in 1829, and died in Australia in 1905. Besides these four sons there were in all three daughters:—Elizabeth, afterwards wife of the Rev. David King, D.D.; Anna, who was married to Mr. William Bottomley of Belfast (these two were the eldest of the family), and Margaret, the youngest, who died in childhood. Thus began William Thomson's residence in and connection with the University of Glasgow, a connection only terminated by the funeral ceremony in Westminster Abbey on December 23, 1907.

Professor Thomson himself carefully superintended the education of his sons, which was carried out at home. They were well grounded in the old classical languages, and moreover received sound instruction in what even now are called, but in a somewhat disparaging sense, modern subjects. As John Nichol has said in his letters, "He was a stern disciplinarian, and did not relax his discipline when he applied it to his children, and yet the aim of his life was their advancement."