Editor's Note: This excerpt is from the first chapter of From Stars to Stalagmites: How Everything Connects, by Paul S. Braterman. Earlier in the chapter the author discusses the ideas among geologists in the 19th century that physical processes such as erosion had always occurred at the same rates and that the features of Earth were static, leading them to conclude that the planet had had no beginning nor would it have an end. Here he writes about how the ideas of physicist William Thomson would end up turning those theories on their heads, paving the way for our current understanding of Earth's early history and age.

Other developments, however, were to undermine this view. I have already mentioned steam engines and railways. Science in the mid 19th century was much occupied with matters concerning work and energy, and the efficiency of heat engines. This period saw the development of a new subject, thermodynamics, dedicated to such matters. One of the most fundamental results of thermodynamics (the First Law) is that energy is conserved. Another (the Second Law) is, that since energy tends to spread out and degrade irreversibly over time, there could be no such thing as a perpetual motion machine. Any real process, and certainly such a process as the uplift and erosion of the Earth, is operating against friction, with overall irreversible degradation of energy into heat, and this is something that cannot continue on its own indefinitely. Yet the Earth, as seen by Hutton and Lyell, appeared to be just one such machine, running through cycles of uplift and erosion with no visible source of energy to drive the process. Conflict between the thermodynamicists and the geologists was inevitable.

William Thomson, Lord Kelvin, in whose honour the absolute temperature scale is now named, was among the most distinguished scientists of the late 19th century. His work straddled the boundary between pure and applied research. Among other things, he played a major role in establishing the relationships between heat, work, and electricity, worked out the theory for how much information (as we would now say) could be carried by the first submarine cable, and improved the form of the compass and the methods of navigation. He was appointed Professor of Natural Philosophy (i.e. Physics) at Glasgow University when he was 22, and held that Chair for more than 50 years.

Kelvin was interested in the age of the Earth, considered as a problem in physics, from a very early stage. It was the subject of a prize undergraduate essay, and also of his inaugural lecture at Glasgow, now unfortunately lost. He was also a sharp critic of the science of geology as it was developing. He argued (correctly) that extreme uniformitarianism was not compatible with the laws of physics. Things must have been very different at some time in the past, and would be different again in the future. The Earth was losing heat and must have once been a molten ball. The Sun was emitting energy, could not have been there forever, and must eventually run out of energy, plunging the Earth into utter cold and darkness.

In a lengthy series of publications, Kelvin attempted to quantify these general objections. He developed a way of estimating the age of the Earth’s solid crust from cooling arguments. It is hot down a mine, and the deeper you go, the hotter. If you could go down deep enough, you would, at a depth of some miles, reach the Earth’s mantle, where the rock is actually molten. So if we have cooler rocks on top and hotter rocks lower down, heat must be flowing up through the rocks from the centre outwards. Knowing how fast the temperature increases as we go down, and how effectively the rocks of the crust conduct heat, Kelvin calculated how fast the Earth was losing heat. Where was this heat coming from? Kelvin thought he had the answer. He assumed (correctly) that the Earth was originally molten, and that heat must have dissipated as the Earth’s rocks solidified from an originally molten state (the opposite kind of process to ice absorbing heat as it melts). From an estimate of the thickness of the solid rock layer (the crust), and from measurements of how much heat it takes to melt a given amount of rock, he was able to estimate how much heat has been given out by this process of solidification. Then, by running the model backwards through time, he calculated that the thickness of the Earth’s solid crust corresponded to 100 million years. At this date before the present, all the rocks now on the surface would have been molten, and this, according to his argument, is therefore an absolute upper limit on the age of the solid crust of the Earth.

Throughout the 19th century, unaware of this approaching crisis, geologists worked away at establishing our familiar geological column. They worked out the order of the strata from which lay on top of which others, and later from the complexity of the fossils they contained, and made estimates of the duration of each geological period from the thicknesses of its best preserved sediments. Not realising that they had only a very incomplete part of the total depositional record, they came up with an estimated age of around 100 million years upwards, in tolerable agreement with Kelvin.

The age of the Sun presented a much more serious problem. We know how large the Sun is, how far away, and how much solar energy reaches us. From this, it is relatively straightforward to calculate its total energy output. Where is this energy coming from? Not from any chemical process, for no chemical process is energetic enough. So Kelvin, building on suggestions by Helmholtz and others, suggested that  a more  useful source might be the gravitational energy released during the Sun’s formation. Knowing the total mass of the Sun, and using Newton’s Laws of gravitational attraction, Kelvin could work out how much energy must have been given out by this process. This would first be converted into the kinetic energy of the infalling matter, and that kinetic energy would then by well-known physical processes be converted to heat and ultimately to light, all in strict obedience to the laws of thermodynamics. Divide the amount of energy available by the rate of output, and you get an upper probable limit of 100 million years for the Sun’s total productive life. This is also, by implication, an upper limit to the age of the Earth as we know it. "As for the future, we may say, with equal certainty, that inhabitants of the Earth can not continue to enjoy the light and heat essential to their life for many million years longer unless sources now unknown to us are prepared in the great storehouse of creation." Kelvin wrote these words in 1862, and published them in a popular journal (Macmillan’s Magazine).

In subsequent refinements of this calculation, he would add  further arguments, based for example on tidal friction and the dynamics of the Earth–Moon system, and in the light of fresh information about the thermal properties of rocks lower the range to some 20–40 million years, "and probably much nearer 20 than 40."

The impact was sensational. For by this time, as Kelvin well knew, a great deal was at stake. Darwin’s Origin of Species had appeared just three years before the Macmillan’s Magazine article. This had revolutionised our perspective on the world. It stated for the first time with complete clarity the modern view that species were not separately created but had evolved from simpler common ancestors by the operation of natural selection on the variations between individuals. The origin of these variations (what we now call mutations) was completely unknown, but it was clear that descent from a common ancestor must have been an extremely slow process, requiring what Darwin himself had described as "incomprehensibly vast… periods of time", with 20 to 40 million years much too little for all this to have occurred by natural selection. Nor did it help when Kelvin revised his 100 million year estimate of the age of the Earth sharply downwards, in the light of new evidence about the melting points of rocks. Indeed, Charles Darwin referred to Kelvin as an "odious spectre" and among his sorest troubles, and his son George was among the geologists most concerned with trying to find flaws in Kelvin’s reasoning.

Reprinted from From Stars to Stalagmites: How Everything Connects, by Paul S. Braterman, with permission from World Scientific Publishing (U.K.), Ltd. Copyright © Paul S. Braterman, 2012.