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 chemical 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 are.

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., T*he
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*. 3rd
ed., Cambridge, MA: Phlogiston Press, 2004, **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.

From Kelvin's collected papers,
1890

Lord Kelvin's calculation of Earth's age

From Light, Visible and Invisible,
1923

This odd photo turned up in an old book about
light.

It is an actual X-ray of Lord Kelvin's hand!

From *Electrivity in Everyday
Life*, 1904

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.

The Engines of Our Ingenuity is
Copyright © 1988-2000 by John H.
Lienhard.