### Changing Views on the Age of the Earth

[Image credit: NASA]

In 1650, the Earth was 4654 years old. In 1864 it was 100 million years old. In 1897, the upper limit was revised to 40 million years. Currently, we believe the age to be about 4.5 billion years. What will be the best guess in the year 2050? [TM217 or search for “thatsmaths” at irishtimes.com].

Ussher’s Chronology

Archbishop James Ussher (1581–1656).

By analysis of the genealogical records in the Scriptures, a chronology of the Earth can be deduced. The most renowned biblical analysis was that of James Ussher, Archbishop of Armagh, Primate of All Ireland and Vice Provost of Trinity College Dublin. In 1650, he stated, with remarkable precision, that the first day of creation was Sunday, October 23, 4004 BC.

We may smile at this, but biologist and popular science writer Stephen Jay Gould defended Ussher’s chronology as “an honourable effort for its time”, writing that Ussher’s work represented the best scholarship of the day. Young Earth creationists still accept Ussher’s chronology as reasonable, but most scholars regard it as a grave under-estimate.

Kelvin and Fourier’s Equation

Belfast-born William Thomson (Lord Kelvin) was Professor of Natural Philosophy at the University of Glasgow for more than 50 years. He made great advances in many areas, both theoretical and practical. When just 16 years old in 1840, Kelvin studied Joseph Fourier’s book The Analytical Theory of Heat. He later wrote “I took Fourier out of the University Library and in a fortnight I had mastered it.” His first scientific paper (under the pseudonym P.Q.R.) was published the following year. The physics of heat remained a lifelong research focus for Kelvin. The unit of absolute temperature was later named in his honour.

William Thomson, Lord Kelvin (1824 –1907).

In 1864, Kelvin estimated the Earth’s age by treating it as a sphere with molten rocks in its interior, gradually cooling by loss of heat from the surface. He assumed that, at the time of its creation, the Earth was at a uniform high temperature. As heat was radiated away from the surface, a gradient from the cooler surface to the hotter interior caused a flow of heat outwards.

The flow of heat is governed by the thermal diffusion equation derived by Fourier. Using measurements of the increase of temperature with distance below ground, and knowledge of thermal conduction rates for various rocks, Kelvin was able to solve this equation,

$\displaystyle{ \frac{\partial T}{\partial t} = \kappa \nabla^2 T \,,}$

and produce an estimate of the time that had elapsed since the temperature of the spherical Earth was uniform.

His best estimate of the age was 100 million years but, given the many uncertainties in the melting points, thermal conductivities and specific heats of rocks, he gave a range from 20 to 400 million years. Over the following decades, Kelvin refined his estimate and, in 1897, he proposed that the Earth was 20–40 million years old. There was major controversy about the Earth’s age. Geological evidence pointed strongly to a value far above Kelvin’s estimate. One of Kelvin’s staunchest opponents was Carlow-man John Tyndall.

Kelvin was unaware of radioactive decay, which provides a source of heat in the Earth’s interior. This was not discovered until 1903. The following year, physicist Ernest Rutherford presented arguments that this additional energy source invalidated Kelvin’s estimates; Kelvin was an attendee at the lecture. This idea was confirmed after the development in 1907 of radiometric dating. This technique is now our main method of dating rocks and fossils. A zircon crystal found in Western Australia has been dated to 4.4 million years ago. Moon rocks returned by the Apollo and Luna missions have been dated to a similar age.

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That’s Maths II: A Ton of Wonders

by Peter Lynch now available.
Full details and links to suppliers at
http://logicpress.ie/2020-3/

>>  Review in The Irish Times  <<

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