Today, a Victorian scientist miscalculates the age of the earth. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

For centuries, Biblical scholars tried to calculate Earth's age. By the mid-nineteenth century, scores of such calculations were extant. They ranged from 5400 to almost 9000 years.

Long before Darwin, geologists had begun insisting that the Bible was never meant to give us that kind of data -- that Earth is, in fact, far older. At first they had no basis for making their own estimates. Then, in 1862, Lord Kelvin made the first numerical calculation of Earth's age based on data outside the Bible.

Kelvin knew that Earth's temperature increased one degree Fahrenheit for each fifty feet you go into the ground. He guessed that Earth began as molten rock at seven thousand degrees Fahrenheit. Then he calculated how long it would've had to cool to establish that surface temperature gradient. He found it must've taken a hundred million years to reach one degree every fifty feet.

But Kelvin's mathematics opened him up to assault by other scientists. In 1807 Joseph Fourier had written a theory of heat conduction based on avant-garde math that many people had trouble accepting. The French Academy suppressed Fourier's theory for thirteen years before they published it. And, once it was published, controversy continued to cloud it. Then Kelvin had to invent radical means for solving Fourier's equation without knowing the conditions deep inside the earth.

So the fat was in the fire! The deeply religious and anti-evolutionist Kelvin had used radical math to calculate an age that was far too *young* to satisfy geologists and Darwinists. But it was *plenty old *enough to waken the ire of Biblical literalists.

The problem with Kelvin's estimate was that he had no way of knowing that radioactive decay keeps resupplying heat. That meant his cooling calculation couldn't possibly have given useful results. Its real value lay in the intellectual stimulus it created.

Of course his critics had no more knowledge of radioactivity than he did. The great Victorian scientists and mathematicians knew *something* was wrong, but *what*? So they formed ranks to fight about questions of mathematical method and Biblical exegesis. The debate went on until the twentieth century. It drew in the likes of Darwin, Huxley, and Heaviside. When they were through fighting, at least heat conduction analysis had found a solid footing.

Today, modern analysis shows that Earth is four and a half *billion* years old. Still, debate over Kelvin's calculation helped to set up means by which engineers can solve far nastier heat-flow problems than he ever could -- means for determining everything from how long it takes to refrigerate fruit to how to cool a brake shoe. So I rather like this checkered story.

It's clear that real understanding is always hard to come by. We need to pass through briar patches like this one if we ever hope to come out wiser than we were.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

Nahin, P., P. J., Kelvin's Cooling Sphere: Heat Transfer Theory in the 19th Century Debate over the Age-of-the-Earth, *History of Heat Transfer: Essays in Honor of the 50th Anniversary of the ASME Heat Transfer Division* (E. T. Layton and J. H. Lienhard, eds.). New York: ASME, 1988, pp. 65-85.

For Fourier's theory, see Fourier, J., *The Analytical Theory of Heat.* New York: Dover Publications, Inc., 1955.

For a simplified version of the so-called semi-infinite region solution to the heat conduction equation (which Kelvin had to create to solve Fourier's equation knowing conditions only at Earth's surface), see J. H. Lienhard IV and J. H. Lienhard V, *A Heat Transfer Textbook*. 4th ed. **Click here for a free copy**. Section 5.6.

Listener Keith Mahon has written me to point out two studies done in the late 1980s showing that radioactive decay is also insufficient to account for the existing steep temperature gradient at Earth's surface. The more plausible cause appears to be thermal convection caused by the movement of plate tectonics. Dr. Mahon provides two additional references on this matter: Frank M. Richter, "Kelvin and the age of the earth", *Journal of Geology*, 1986, vol. 94, p. 395-401, and T. Mark Harrison, "Comment on 'Kelvin and the age of the earth'", *Journal of Geology*, 1987, vol. 95, p. 725-727.

This is a greatly revised version of Episode 144.

Lord Kelvin's calculation of Earth's age

From Kelvin's collected papers, 1890

This odd photo turned up in an old book about light. It is an actual X-ray of Lord Kelvin's hand!

From *Light, Visible and Invisible*, 1923

And here is Kelvin himself. From left to right: George Westinghouse, Lord Kelvin, and Charles Merz. They are observing a machine for changing ac to dc.

From *Electrivity in Everyday Life*, 1904