"High up in the North in the land called Svithjd, there stands a rock. It is hundred miles high and a hundred miles wide. Once every thousands years a little bird comes to this rock to sharpen its beak. When the rock has been thus worn away, then a single day of eternity will have gone by."
Norwegian folktale as recounted by Hendrik Van Loon in "Story of Mankind"
In the early 19th century the idea of an old earth became rapidly accepted, based on the observation that most processes on earth, like formation and erosion of mountains, occur slowly. Also Charles Darwin observations in biology confirmed the geological timescale. As evolution occurs over thousands, maybe millions of generations, to explain the recent biodiversity and specialization also earth had to be thousands, maybe million of years old - not even considering global extinction events and the successive period of recovery.
But how old is earth exactly and how can we know?
The British astronomer Edmund Halley (1656-1742) suggested in 1775 that a minimum age of the oceans (and therefore earth) could be estimated by measuring the input of dissolved elements by rivers and the resulting increase in salinity. However lacking precise measurements this idea remained a hypothetical approach. Benoit De Maillet (1656 - 1738), French consul in Egypt, proposed, based on his observations of the sea level drop along the Egyptian coasts, that earth was completely inundated 2.000 million years ago.
In 1774 the French naturalist Georges-Louis Leclerc, Comte de Buffon (1707-1788) published in the "Histoire Naturelle" the results of his experiments with cooling iron spheres. Based on the popular hypothesis that earth formed from a molten sphere of condensated interstellar matter, he used the cooling time of incandescent iron spheres to calculate the age of the (solid parts) of the globe. Buffon's published results gave an age of 75.000 years for the last creation (Buffon proposed a succession of various epochs of animal life, based on his knowledge of past mass extinctions), however from unpublished notes, where he address the problems and speculations concerning his calculations, it seems that Buffon considered a much older earth - million of years in the making - possible.
James Hutton had in 1785 successfully argued that the deposition of layers need long time periods, however he considered any exact age estimates as mere speculation. Later geologists were more confident and based on the thickness and erosion rates of rock formations tried to calculate the age of earth.
Darwin estimated from the thickness of geological formations of the Wealden region an age of 300 million years. One of Britain's leading geologists, Sir Archibald Geikie (1835-1924), used the height of mountains and denudation rates to calculate the age of continents. According to his calculation, North America would be eroded away in 4,5 million years and Europe would last for just 4 million years, if there are no processes forming new mountains. Charles Lyell published ages ranging from 20 to 240 million years based on the supposed time intervals needed for certain mollusc-assemblages to become replaced in the fossil record. In 1899 the British physicist and geologist John Joly (1857 - 1933) calculated, based on the salinity of the great oceans, a time interval of 90 million years to transform the primordial freshwater into saltwater.
Physicist William Thomson, 1st Baron Kelvin (1824-1907) became interested in the question of the age of earth by his studies on the physicals properties of the sun. Kelvin calculated the energy dispersal of the sun (which he considered made of an incandescent liquid) and concluded that sun was between 400 to 20 million years old, favouring in the end the younger age. As the possible age of earth was constrained by the age of the sun most of the ages postulated by geologist were erroneous - so it seemed at the time... to be continued.
JACKSON, P.W. (2006): The ChronologersQuest - The Search for the Age of the Earth. Cambridge University Press: 291
LEDDRA, M. (2010): Time Matters - Geologys Legacy to Scientific Thought. Wiley-Blackwell: 269
LEWIS, C.L.E. & KNELL, S.J. (eds.) (2001): The Age of the Earth: from 4004 BC to AD 2002. Geological Society Special Publication No. 190: 288