While the phrase “pressed on my mind” was somewhat of an overdramatized exaggeration, it was certainly true that Kelvin’s first papers on the topics of heat conduction and the distribution of heat through the body of the Earth were written as early as 1844 (when he was a twenty-year-old student) and 1846, respectively. Even before his seventeenth birthday, Thomson succeeded in spotting a mistake in a paper on heat by an Edinburgh professor.

Kelvin’s point was simple: Measurements from mines and wells indicated that heat was flowing from the Earth’s interior to its surface, implying that the Earth was an initially hotter planet that was cooling. Consequently, Kelvin argued, unless some internal or external energy sources could be shown to compensate for the heat losses, clearly no steady state, or repeating, identical geological cycles, were possible. Charles Lyell was actually aware of this problem, and in his Principles of Geology he proposed a self-sustaining mechanism by which he believed that chemical, electric, and heat energy could be exchanged cyclically in the Earth’s interior. Basically, Lyell envisaged a scenario in which chemical reactions generated heat, which drove electrical currents, which in turn dissociated the chemical compounds into their original constituents, thus starting the process anew. Kelvin could barely hide his contempt. He demonstrated unambiguously that such a process amounted to some sort of perpetual motion machine, violating the principle of dissipation (and conservation) of energy—when mechanical energy is transformed irreversibly into heat, as in the case of friction. Lyell’s mechanism therefore violated the basic laws of thermodynamics. To Kelvin, this was the ultimate proof that the geologists were completely ignorant of physical principles, and he remarked caustically:

To suppose, as Lyell, adopting the chemical hypothesis, has done, that the substances, combining together, may be again separated electrolytically by thermoelectric currents, due to the heat generated by their combination, and thus the chemical action and its heat continued in an endless cycle, violates the principles of natural philosophy in exactly the same manner, and to the same degree, as to believe that a clock constructed with a self-winding movement may fulfill the expectations of its ingenious inventor by going for ever.

At its core, Kelvin’s calculation of the age of the Earth was straightforward. Since the Earth was cooling, he explained, one could use the science of thermodynamics to calculate the Earth’s finite geological age: the time it took the Earth to get to its current state, since the formation of the solid crust. The idea itself was not entirely new; the French physicist Joseph Fourier had developed the mathematical theory of thermal conductivity and of the Earth’s cooling process at the beginning of the nineteenth century. Realizing the theory’s potential, Kelvin engaged in 1849 in a series of measurements of underground temperatures (together with the physicist James David Forbes), and in 1855 urged that a complete geothermal survey be conducted, precisely to enable the calculation of the Earth’s age.

Kelvin assumed that the mechanism that transported heat from the interior to the surface was the same type of conduction that transfers heat from an iron skillet on an open fire to its handle. Still, in order to apply Fourier’s theory to the cooling Earth, he needed to know three physical quantities: (1) the initial internal temperature of the Earth, (2) the rate of change in the temperature according to depth, and (3) the value of the thermal conductivity of the Earth’s rocky crust (which determines how fast heat can be transported).