Yeshu Kolodni and Lord Kelvin

### The question

In 1862, the physicist William Thomson (who later became Lord Kelvin) of Glasgow published calculations that fixed the age of Earth at between 20 million and 400 million years. Later in the 1890s Kelvin calculated the age of Earth by using thermal gradients, and arrived at an estimate of 100 million years old which he later reduced to 20 million years. (For much more interesting details see this Wikipedia article.)

The question was: what was the main reason for Lord Kelvin’s wrong estimation

a) Radioactivity – Heat produced by radioactive decay; this was a process unknown to science for decades to come.

b) Convection – The transfer of heat not through radiation or heat-conduction but through the movement of hot parts to the surface; this is a process familiar in home cooking.

Here is the answer and some discussion mainly based on what Yeshu Kolodny have told me.

### The short answer: Convection

The short answer is that the main mistake in Lord Kelvin’s estimates was **convection. **

This was also the most popular answer in our poll with 48%, radioactivity got 44%, and 6% voted for both these elements have similar effect.

### The longer answer and Kelvin’s computation of the age of the sun

There is more to be said, of course. And let me from now on simply quote what Yeshu told me directly:

“Kelvin (previously Thomson) was certainly one of the greatest physicists and engineers of the 19th century. He directed the laying of the first transatlantic telegraph cable, formulated the second law of thermodynamics and wrote hundreds of influential papers. At very young age he was one of the first to study and understand Fourier’s heat-flow treatment, and it is this that led him to calculating first the **age of the sun**, then that of the earth. In the age of the sun a major error was obviously neglecting heat production by nuclear reactions; in the age of he earth – convection.

Kelvin assumed that the source of the Sun’s energy was gravitational – a collapse (accumulation) of many meteors, and thus conversion of mechanical energy into heat (Joule’s heat equivalent was already known). This way he calculated the Sun’s age first to be around 32 millions years, later put an upper limit of 300 million years and a “most probable age of 100 million years). Kelvin (correctly) assumed that the earth cannot be older than the sun, and is most likely of the same age. The prevalent hypothesis for the formation of Sun and planet formation was that of Kant-Laplace, which involved the above-mentioned “nebular hypothesis” (an improved version of it is still accepted today). So when he got the “age of the earth” to be within error of what he assumed to be the “age of the sun” both arrived by different approaches, he was very happy.

### The geologists victory and where was Lord Kelvin right

It is rather impressive that this genius of physics was opposed by a bunch of geologists (high boots, shorts, field hammers, limited perspective) and that the latter turned out right, but it is also true that Kelvin showed two important points:

The first is that the age of the earth is NOT INFINITE as many thought in the 19th century, and the second is that the age of the earth is calculable from physical principles. At that time, several geologists claimed that “physics cannot be applied to geology,” and in this they were wrong! We owe him much for teaching us these two points.”

What an exciting, spirit-lifting story it is! And there are more facets to it. Of course, radioactivity played a major role in modern estimates for the age of the earth.

As far as I remember, the Kelvin’s calculation of the age of Sun was almost instantly contested by astronomers. In order to maintain the observed energy balance, the Sun should have been bombarded by meteors with such intensity that its mass would be growing quite noticeably, affecting the periods of rotation of planets (e.g., the terrestrial year), which was in contradiction with observations.

(I remember this story from Isaac Asimov’s book “The Universe: from flat Earth to Quasars” which was probably the best reading in astronomy for kids at the age 13+ when I was there…)

<a href="http://www.americanscientist.org/issues/page2/kelvin-perry-and-the-age-of-the-earth" Here is the original article. Very interesting.

Thanks Sergei and Peter. Among the other facets to this story are of course the connection to evolution, that required a much longer age for the earth, and the mathematical models for convection which came much later and were closely related to the debate regarding continental drifts. Yeshu mentioned Chaim Leib Pekeris among those who developed mathematical models for convections.