Kelvin was able to obtain a rough estimate: This timescale is known today as the Kelvin-Helmholtz timescale.

“It seems, therefore, on the whole”: Kelvin 1862. Shaviv 2009 presents a very detailed but quite accessible exposition of the theory of stellar structure and evolution.

Kelvin later described the conversation: Thomson 1899. Chamberlin 1899 presents a commentary on Kelvin’s address in 1899.

when Kelvin delivered an address: On February 27, 1868; Kelvin 1891–94, vol. 2, p. 10.

“The earth, if we bore into it”: Kelvin 1891–94, vol. 2, p. 10.