## Sunday, January 23, 2011

### The beginning of the discovery

Charles Fourier was a scientist and mathematician, who was fascinated by the flow of heat and determining how heat flow occurs.

His main paper was Théorie analytique de la chaleur (The Analytic Theory of Heat) in 1822. He claimed that any function or variable, continuous or discontinuous, could be expanded in a series of sines of multiples of the variable. This is not quite correct, but some discontinuous functions are the sum of a series, and that was a breakthrough.
Fourier's idea was that the flow of heat between two molecules is proportional to the extremely small difference in temperature between adjacent molecules.

His interest in heat lead him to this inquiry---why doesn't the sun just heat the Earth up until the Earth's temperature match the surface of the sun?

The answer was that heat radiates away from the Earth, preventing the Earth from heating up catastrophically. However there was a serious problem.

There had been some attempts to determine what the equilibrium temperature of the surface of the Earth should be, notably by Georges-Louis Leclerc Comte de Buffon and his attemps, and others, indicated that the Earth should be colder than it really is.

When Charles Fourier used his new equations, he came up with temperatures between 0F and 5F. Most of the world would be frozen! (This actually understates the degree of cold considerably. If the world was really that coldm the ice covered oceans and snows to the equator would increase the albedo of the Earth sufficiently to cool the Earth down to ~-50C on average.

Something else was clearly going on, but he was not sure what. The heat equations he was sure were right (and they largely were). What was going on?

One idea (the right one) was that the atmosphere was partly opaque to Herschel's newly discovered infrared rays. This would require most of the energy of the sun to arrive as visible light or other ways and warm the Earth. At the same time some of the IR radiation emitted by the warm earth would be trapped in the atmosphere and warm the earth enough for it to reach its current equilibrium temperature.

Fourier didn't know if this was a general property or the result of minor gases in the atmosphere.

But Fourier was led astray by another idea.

Olber's Paradox (why isn't the sky bright as the sun, and why isn't the whole universe at the same temperature as the suns) made a big splash in 1823. Heinrich Wilhelm Olbers considered if the universe was infinitely big, every line of sight would end up on the surface of a star. So why isn't the entire sky as bright as the surface of the sun?

Nebulas wouldn't help. They would be heated from all directions till they were as hot as the surface of suns as well.

Olber's paradox contains some hidden assumptions. The universe is infinitely big. The universe is not expanding. The speed of light is infinite. Or if the speed of light is finite, the universe is infinitely old.

The speed of light was known to be finite by 1823. Which meant that the universe could not be both infinitely old and infinitely big. Olber's paradox is the first scientific inquiry that showed there had to be limits on either the size or the age of the universe. Which implied that either the size of the universe or its age, or both, were bound by limits--and a limited figure could be determined.

Heinrich Wilhelm Olbers was not the first to come up with this paradox. There were even some before him who made superior mathematical treatments of it.

However, for some reason or another, his publication of this idea made a big splash.

Olbers also discovered the asteroid Pallas, the second asteroid found (1802) and Vesta, the brightest asteroid and the fourth discovered.

Olber's paradox mislead Fourier. Fourier believed the warmth of the earth could be explained if space were not close to absolute zero, but if the interstellar voids were warm. Instead of temperatures dropping asymptotically towards absolute zero (or 2.7K) as one gets further from the sun, what if the temperature dropped asymptotically to 100K? or 150K? Then the warmth of the earth would fit. Interstellar radiation could be responsible for the warm Earth! (Yes I know there was no Kelvin scale yet in the 1820s, but you get the idea)

Charles Fourier's main papers on the subject of the temperature of the earth were Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires (General Remarks on the temperatures of the terrestrial globe and planetary spaces) [1824] and Mémoire Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires (Disseratation on the Temperatures of the Terrestrial Globe and interplanetary spaces) [1827]

While Charles Fourier discussed the idea of the atmosphere warming the earth by selectively trapping infrared radiation, he was strongly influenced by Olber's paradox and believed the warm baseline temperature of interstellar space to be responsible. A pity.

Charles Fourier referred to an experiment by Horace-Bénédict de Saussure in his papers. He was also interested in heat, and may have developed the first solar oven. Saussure performed an experiment with a box of black cork, with three pane of glass 1 1/2" apart, and measured the temperature between each pane. The temperature increased the more interior one checked in the box. This box with panes of glass was like a greenhouse in some ways, and lead to references of the "greenhouse effect"

So for all you who think the "greenhouse effect" is some insidious French plot---let the conspiracy yarns start!

Fourier also was ignorant of some important properties of the atmosphere. He thought that eddies and convection would immediately carry heat away from the surface of the Earth--that these eddies went all the way to the top of the atmosphere. Today we know that the stratosphere is very stable, with temperatures rising with altitude, the opposite of the troposphere we live in. This also lead him to look on the atmospheric 'greenhouse effect' with disfavor.

1. Georges-Louis Leclerc, Comte de Buffon (Comte = Count, and don't you dare forget it!) was a very interesting character. He was the long-time director of the Jardin du Roi (Garden of the King) from 1739-1788. I said it was a loooooong time. The Jardin du Roi was more like a research institution than a mere garden.

Buffon had long been interested in the legendary defense of Syracuse against the Romans by Archimedes. Archimedes was supposed to have set up giant mirrors that reflected and focused the sun onto the Roman ships, setting them aflame.

There was (and is) a lot of skepticism about this, and the great Descartes said it couldn't be done.

But Buffon was out to prove them all wrong.

In 1747 he made his splash. He assembled 4 huge wooden frames supporting an array of more than 150 mirrors, aligned by screw threads, to focus the sunlight on a plank of wood 158 feet away. Within 2 minutes, the wood began to char and then alors! A cloud moved over. But Buffon had seen enough to know it would work. Later than summer he wowed crowds as he set fire to buildings over 200 feet away. He arranged a personal demonstration for King Louis XV, and Frederick the Great of Prussia sent his personal congratulations.

Georges-Louis Leclerc, Comte de Buffon, had arrived!

2. The Jardin du Roi was more like a natural history research institute than a garden, and Buffon's greatest contributions were as a naturalist. He was quite irreverent, and pissed off the Catholic Church to no end, with his pronouncements of extinctions, and what were then wildly ancient estimates of the Earth's age. He would be summoned, made to repent and then go back to publishing what he wanted. He said "Better a mass than a hanging!" with a mischeivous twinkle in his eye, as if to say just, just.

He was also very full of himself. As we shall see.

He was a 'hemispheric chauvinist' proclaiming the superiority of Old World fauna versus the new world, leading to heated, but ultimately civil correspondence with Thomas Jefferson.

3. Georges-Louis Leclerc, Comte de Buffon wanted to find out the age of the earth. He absolutely revolted at the idea that stuffy French clerics were the end all and be all in scientific authority. Less than 5,800 years old?! Ridiculous!

But how to determine the age of the Earth?

Buffon thought that this would be easy to determine. It wasn't

It had been pointed out that the odds of all the planets orbiting in the same direction was 2 to the 6th power, or 64 to 1. At the time it was believed that all the planets' orbits were within 7 1/2 degrees of each other, yielding stupendous odds of 7,962,624 to 1.

Newton believed that the planets had been set into motion by "the counsel and dominion of an intelligent and powerful being" [God].

Buffon had no need for God. He thought the planets had been thrown off 'splashed' the sun by a giant comet.

But how long would it take solar material to condense into the Earth and cool so we have the planet we see today?

Buffon didn't have Fourier's mathematical tools to determine heat dissipation. Instead, he chose another method.

4. Buffon's idea was to heat up balls of iron, clay, various types of stone in a kiln. A ball of tin in the kiln served as a crude thermometer. When it started to melt, take the balls out. But how to measure how they cooled?

Buffon employed several "very pretty" women with soft, delicate skin to hold the balls and describe how long it took them to cool down, holding Buffon's [metal, stone or whatever] balls at intervals until they cooled to room temperature.

This being France, the very idea that there was anything improper about Buffon asking pretty, delicate-skinned young girls to hold his balls is of course preposterous.

Based on this imprecise measuring method Buffon decided that the rate of cooling is proportional to the diameter of a sphere.

That is wrong, so very wrong. The rate a sphere loses heat is determined by the square of the diameter. A sphere twice the diameter of another has 8 times the mass, but only 2 times the surface area. So a sphere twice the size of another takes 4 times as long to cool, 3 times the diameter 9 times as long, etc.

But Buffon calculated his figures, and he came up with 74,047 years to reach the current temperature of the Earth. But wait! The Earth was still receiving energy from the sun! So he made another 150 pages of calculations, and came up with another 785 years for the earth to cool. So in 1779 when Buffon published his Epochs of Nature he described the Earth as being 74,832 years old.

5. This wasn't quite the end, however. Buffon had been working on his book for years, and what really took so long was massaging his data. In his private manuscripts, he believed the world to be 10 million years old. But that was so shocking a figure in 1779 that he spent years creating equations and figures and results that would rationally result in a more reasonable figure of 74,832 years old.

6. Buffon tried to compute what the average temperature of the Earth should be at equilibrium. As said before, he didn't have Fourier's mathematical tools, but his own equations all showed that the Earth should be cooler than it is.

Buffon thought that the warmth of the earth was residual heat from the condensing solar matter. And that the Earth would continue to slowly cool.

Buffon was the first to perceive that the Earth is warmer than it should be, although the greenhouse effect never occurred to him.

Because Buffon thought the Earth was cooling with time, he thought it was in Russia/Siberia that humanity and civilization began. Catherine the Great, Queen of Russia, was so gratified that Buffon placed Russia as the origin of civilization that she sent Buffon a stream of gold, jewelry and furs.

In return, Buffon sent his son to St. Petersburg to present Queen Catherine the Great with a bust--of himself!