Cambridge

William's father was able to make a generous provision for his favourite son's education and, in 1841, installed him, with extensive letters of introduction and ample accommodation, at Peterhouse, Cambridge. In 1845 Thomson graduated as Second Wrangler.^[11] He also won a Smith's Prize, which, unlike the tripos, is a test of original research. Robert Leslie Ellis, one of the examiners, is said to have declared to another examiner You and I are just about fit to mend his pens.^[12]

While at Cambridge, Thomson was active in sports, athletics and sculling, winning the Colquhoun Sculls in 1843.^[13] He also took a lively interest in the classics, music, and literature; but the real love of his intellectual life was the pursuit of science. The study of mathematics, physics, and in particular, of electricity, had captivated his imagination.

In 1845 he gave the first mathematical development of Faraday's idea that electric induction takes place through an intervening medium, or "dielectric", and not by some incomprehensible "action at a distance". He also devised a hypothesis of electrical images, which became a powerful agent in solving problems of electrostatics, or the science which deals with the forces of electricity at rest. It was partly in response to his encouragement that Faraday undertook the research in September 1845 that led to the discovery of the Faraday effect, which established that light and magnetic (and thus electric) phenomena were related.

He was elected a fellow of St. Peter's (as Peterhouse was often called at the time) in June 1845.^[14] On gaining the fellowship, he spent some time in the laboratory of the celebrated Henri Victor Regnault, at Paris; but in 1846 he was appointed to the chair of natural philosophy in the University of Glasgow. At twenty-two he found himself wearing the gown of a learned professor in one of the oldest Universities in the country, and lecturing to the class of which he was a freshman but a few years before.

Thermodynamics

By 1847, Thomson had already gained a reputation as a precocious and maverick scientist when he attended the British Association for the Advancement of Science annual meeting in Oxford. At that meeting, he heard James Prescott Joule making yet another of his, so far, ineffective attempts to discredit the caloric theory of heat and the theory of the heat engine built upon it by Sadi Carnot and Émile Clapeyron. Joule argued for the mutual convertibility of heat and mechanical work and for their mechanical equivalence.

Thomson was intrigued but skeptical. Though he felt that Joule's results demanded theoretical explanation, he retreated into an even deeper commitment to the Carnot–Clapeyron school. He predicted that the melting point of ice must fall with pressure, otherwise its expansion on freezing could be exploited in a perpetuum mobile. Experimental confirmation in his laboratory did much to bolster his beliefs.

In 1848, he extended the Carnot–Clapeyron theory still further through his dissatisfaction that the gas thermometer provided only an operational definition of temperature. He proposed an absolute temperature scale^[15] in which a unit of heat descending from a body A at the temperature T° of this scale, to a body B at the temperature (T−1)°, would give out the same mechanical effect [work], whatever be the number T. Such a scale would be quite independent of the physical properties of any specific substance.^[16] By employing such a "waterfall", Thomson postulated that a point would be reached at which no further heat (caloric) could be transferred, the point of absolute zero about which Guillaume Amontons had speculated in 1702. Thomson used data published by Regnault to calibrate his scale against established measurements.

In his publication, Thomson wrote:

... The conversion of heat (or caloric) into mechanical effect is probably impossible, certainly undiscovered

— But a footnote signalled his first doubts about the caloric theory, referring to Joule's very remarkable discoveries. Surprisingly, Thomson did not send Joule a copy of his paper, but when Joule eventually read it he wrote to Thomson on 6 October, claiming that his studies had demonstrated conversion of heat into work but that he was planning further experiments. Thomson replied on 27 October, revealing that he was planning his own experiments and hoping for a reconciliation of their two views.

Thomson returned to critique Carnot's original publication and read his analysis to the Royal Society of Edinburgh in January 1849,^[17] still convinced that the theory was fundamentally sound. However, though Thomson conducted no new experiments, over the next two years he became increasingly dissatisfied with Carnot's theory and convinced of Joule's. In February 1851 he sat down to articulate his new thinking. However, he was uncertain of how to frame his theory and the paper went through several drafts before he settled on an attempt to reconcile Carnot and Joule. During his rewriting, he seems to have considered ideas that would subsequently give rise to the second law of thermodynamics. In Carnot's theory, lost heat was absolutely lost but Thomson contended that it was "lost to man irrecoverably; but not lost in the material world". Moreover, his theological beliefs led to speculation about the heat death of the universe.

Thomson became scientific adviser to a team with Whitehouse as chief electrician and Sir Charles Tilston Bright as chief engineer but Whitehouse had his way with the specification, supported by Faraday and Samuel F. B. Morse.

Thomson sailed on board the cable-laying ship HMS Agamemnon in August 1857, with Whitehouse confined to land owing to illness, but the voyage ended after 380 miles (610 km) when the cable parted. Thomson contributed to the effort by publishing in the Engineer the whole theory of the stresses involved in the laying of a submarine cable, and showed that when the line is running out of the ship, at a constant speed, in a uniform depth of water, it sinks in a slant or straight incline from the point where it enters the water to that where it touches the bottom.^[26]

Thomson developed a complete system for operating a submarine telegraph that was capable of sending a character every 3.5 seconds. He patented the key elements of his system, the mirror galvanometer and the siphon recorder, in 1858.

Whitehouse still felt able to ignore Thomson's many suggestions and proposals. It was not until Thomson convinced the board that using purer copper for replacing the lost section of cable would improve data capacity, that he first made a difference to the execution of the project.^[27]

The board insisted that Thomson join the 1858 cable-laying expedition, without any financial compensation, and take an active part in the project. In return, Thomson secured a trial for his mirror galvanometer, about which the board had been unenthusiastic, alongside Whitehouse's equipment. However, Thomson found the access he was given unsatisfactory and the Agamemnon had to return home following the disastrous storm of June 1858. Back in London, the board was on the point of abandoning the project and mitigating their losses by selling the cable. Thomson, Cyrus West Field and Curtis M. Lampson argued for another attempt and prevailed, Thomson insisting that the technical problems were tractable. Though employed in an advisory capacity, Thomson had, during the voyages, developed real engineer's instincts and skill at practical problem-solving under pressure, often taking the lead in dealing with emergencies and being unafraid to lend a hand in manual work. A cable was finally completed on 5 August.

In 1884, Thomson delivered a series of lectures at Johns Hopkins University in the United States in which he attempted to formulate a physical model for the aether, a medium that would support the electromagnetic waves that were becoming increasingly important to the explanation of radiative phenomena.^[48] Imaginative as they were, the "Baltimore lectures" had little enduring value owing to the imminent demise of the mechanical world view.

In 1900, he gave a lecture titled Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light.^[49] The two "dark clouds" he was alluding to were the unsatisfactory explanations that the physics of the time could give for two phenomena: the Michelson–Morley experiment and black body radiation. Two major physical theories were developed during the twentieth century starting from these issues: for the former, the Theory of relativity; for the second, quantum mechanics. Albert Einstein, in 1905, published the so-called "Annus Mirabilis Papers", one of which explained the photoelectric effect and was a foundation paper of quantum mechanics, another of which described special relativity.