Any explanation of adaptation by small accumulated changes is a promissory note drawn on a bank account nobody had checked, and the previous lesson ended by naming the currency: time.
The account was checked, and by people with no interest in biology. This lesson follows three separate findings, each established before Darwin published and none of them by him: that the earth is very old, that species go extinct, and that the fossils in the rocks appear in a fixed order that is never inverted. It ends with the first serious mechanism proposed for that order, and with the experiment that killed it.
An earth with no visible beginning
In 1788 James Hutton took two companions by boat to Siccar Point on the Berwickshire coast to show them a rock face. At the bottom are beds of greywacke standing almost vertically. Above them, cut flat across their broken ends, lie beds of red sandstone lying nearly horizontally. To read that face you must accept a sequence: the greywacke was laid down flat under water, buried, tilted to the vertical, lifted above sea level, planed off by erosion, submerged again, and buried again under sand. Every one of those steps happens today at rates you can measure, and none of them is quick.
Hutton's argument, later made systematic by Charles Lyell in the Principles of Geology of 1830 to 1833, is that the processes visible now are enough to account for everything visible in the rocks, given enough time. He would not name the time. What he wrote is that the record shows "no vestige of a beginning, no prospect of an end", which is not a measurement but a refusal to accept one that was too small.
The refusal is quantitative in spirit even when the numbers are missing, and it is worth doing the arithmetic he could not.
Example. The Grand Canyon exposes about 1,800 m of flat-lying sedimentary rock. Marine sediments today accumulate at rates in the range 0.02 to 0.1 mm a year. How long does 1,800 m take?
At 0.1 mm a year, 1,800 m is mm, so the time is years, or 18 million years. At 0.05 mm a year it is 36 million years. Either figure is already four orders of magnitude past the six thousand years then commonly assumed, and it takes no account of the gaps, of which the canyon has several: below the flat beds lies a tilted sequence and below that a schist, each demanding its own history of burial, deformation and erosion before the beds above began.
Now you. The chalk of southern England is about 500 m thick and is made almost entirely of the skeletons of single-celled algae, which settle at something like 0.03 mm a year. How long was the chalk sea in place?
Answer
years, about 17 million. The modern date for the chalk, from the fossils and from radiometric ages in interbedded ash layers, is roughly 100 to 66 million years ago, which is a span of the right order. The point is not the agreement, which is partly luck given the crudity of the rate. The point is that the calculation is the sort a farmer could do, requires no theory, and gives an answer nobody wanted.
Cuvier proves that species end
The second finding came from a man who spent his career arguing against evolution. On 4 April 1796 Georges Cuvier read a paper to the Institut National in Paris comparing the jaws and teeth of living and fossil elephants. He showed that the Indian and African elephants are two distinct species, not varieties of one; that the Siberian mammoth is a third, differing in the shape of the lower jaw and the enamel plates of the molars; and that the great animal from the Ohio, later named mastodon, is a fourth, with blunt conical cusps rather than plates.
The conclusion is the one nobody had been willing to draw. Elephants are not animals that hide. If the mammoth existed and no mammoth is alive, then a species has ended. Within a few years Cuvier had added the giant ground sloth Megatherium, a marine reptile from Maastricht that he identified as a lizard rather than a whale, and a flying reptile he named Ptéro-dactyle. He was the best comparative anatomist alive, his identifications held, and extinction became a fact.
Cuvier's own explanation was a series of geological revolutions, sudden floods that wiped out faunas which were then replaced by immigration from elsewhere. He rejected transmutation flatly and had a good reason for doing so: the mummified ibises brought back from Egypt were three thousand years old and anatomically identical to living ones, so species were evidently stable on any timescale then imaginable. He was right about the observation and wrong about what it implied, because three thousand years is nothing.
The order in the rocks is fixed
The third finding came from a canal surveyor. Between 1799 and 1815 William Smith worked out that strata in England can be identified anywhere by the fossils in them, that the same assemblage always occurs in the same position relative to other assemblages, and that the order never reverses. His 1815 map of England and Wales was drawn on that principle and is still substantially correct.
This is the principle of faunal succession, and its strength is that it is a very easily broken rule. There are thousands of exposures, on every continent, and every one of them is an independent chance to find an assemblage out of place. None does. Trilobites occur below the first fish and never above the last chalk. Flowering plant pollen appears in the Cretaceous and never below it. Mammals with placentas do not occur in Devonian rocks, and no amount of searching has produced them; J. B. S. Haldane, asked what observation would destroy the theory, is supposed to have said a fossil rabbit in the Precambrian.
Note carefully what succession establishes and what it does not. It establishes that different faunas occupied the same place at different times, in a consistent global order. It does not by itself establish that the later ones descended from the earlier ones: Cuvier read the same order as a sequence of replacements. Succession is a constraint that any theory must fit, not a theory.
Kelvin's objection, which was valid
By the 1860s geologists were speaking freely of hundreds of millions of years, and the best physicist in Britain told them they could not have it. William Thomson, later Lord Kelvin, argued in 1862 that the earth began molten and has been cooling by conduction ever since, and that the temperature gradient measured in mines therefore fixes how long the cooling has run. Deep mines gave about 1 °F per 50 ft, which is 36.4 K per kilometre.
Example. Kelvin's conduction model gives the age as , where is the initial surface temperature, the present gradient and the thermal diffusivity of rock. Take K, K/m and m² per second. What age comes out?
The length m. Squaring gives m², and dividing by m² per second gives seconds. A year is seconds, so the age is years, about 100 million. Kelvin published 98 million with a range of 20 to 400 million, and by 1897 he had narrowed it to between 20 and 40 million. That is not enough time for the geology, let alone the biology, and Darwin called it one of his sorest troubles.
Now you. The calculation is arithmetically correct and its conclusion is wrong by a factor of about a hundred. Where is the error, and what does the episode teach about arguments of this shape?
Answer
Two errors, and the better known is the smaller one. Radioactivity, discovered in 1896, means the earth has a heat source inside it, so the gradient is not the fading trace of an initial store and the clock reads long. The deeper error was identified by John Perry in 1895, before radioactivity was relevant: the model assumes heat moves through the whole earth by conduction, and if the interior convects instead it delivers heat to the base of a cool rigid shell far faster, which reproduces the observed surface gradient at any age you like. Kelvin dismissed him. The lesson is about the shape of the argument: a valid deduction from a measured quantity is only as good as its model of the system, and a physical argument that contradicts a large body of field observation is at least as likely to have a missing term as the field observation is to be wrong.
Putting numbers on it
The resolution arrived with the same discovery that broke the objection. Radioactive decay is a clock: a parent nuclide decays to a daughter at a rate no chemical or physical condition alters, so a mineral that incorporated parent and excluded daughter when it crystallised records its own age in the ratio of the two. Bertram Boltwood applied this to uranium and lead in 1907 and got ages up to 2.2 billion years. Arthur Holmes spent forty years making the method trustworthy. In 1956 Clair Patterson, measuring lead isotopes in the Canyon Diablo iron meteorite, gave the age of the solar system as 4.55 ± 0.07 billion years, a figure that has moved only in its third digit since.
The arithmetic is a rearranged exponential decay. If is the daughter accumulated and the parent remaining, then , so , with .
Example. A zircon crystal contains lead-206 and uranium-238 in the ratio . The half-life of uranium-238 is 4.468 billion years. How old is the crystal?
The decay constant is per billion years. Then billion years. Zircon is used because it takes uranium into its lattice readily and rejects lead almost completely, so the assumption that all the lead-206 present is decay product is a good one, and because it survives metamorphism that resets other minerals.
Now you. A second zircon from the same terrain gives . How old is it, and what does the pair of ages mean?
Answer
billion years. The pair means the terrain contains crystals that formed more than a billion years apart, which is ordinary: an igneous body can pick up older zircons from the rock it intrudes, and those inherited grains keep their own ages. This is why a single date is nearly worthless and a population of dates is informative. The oldest terrestrial zircons, from the Jack Hills of Western Australia, give about 4.4 billion years.
The first mechanism, and the experiment that killed it
With extinction real, succession established and time eventually granted, the field had a fact needing a mechanism. The first serious one was published by Jean-Baptiste Lamarck in Philosophie Zoologique in 1809, and he deserves better than the caricature.
Lamarck proposed two principles. The first is use and disuse: an organ exercised repeatedly develops and strengthens, one neglected weakens and shrinks. That is simply true, and any bodybuilder demonstrates it. The second is that such acquired modifications are passed to offspring. Together they give a mechanism that is genuinely adaptive, since the changes are directed at what the animal actually does, and Lamarck combined it with a separate drive towards complexity to produce the first full theory of transmutation in print.
The second principle is the one that must be tested, and unlike most nineteenth-century biology it is directly testable. August Weismann did the obvious experiment in the 1880s, cutting the tails off mice and breeding them. The reported result is 901 young over five generations, every one with a normal tail. The experiment is often mocked as naive, since nobody claimed that mutilation is an adaptive response, and the criticism is fair; but the theoretical point that replaced it was Weismann's own and it is decisive. In animals the cells that make gametes are set aside early and are not the cells that build the body. Information flows from germ line to body, and there is no return path, so what the body acquires cannot be written back.
The modern qualifications should be stated honestly, because they are real and are routinely overstated. Chemical marks on DNA and its packaging proteins can persist through cell division, and in plants and a few animal cases can survive into the next generation or two. These effects are found, they are usually reset within a couple of generations, and they do not alter the DNA sequence. They are a mechanism for short-term response, not the mechanism for building an eye. Lamarck's fact, that lineages change over time, survived. His mechanism did not.
That leaves the field where the next lesson begins: an old earth, a documented succession of faunas, a proven history of extinction, and no working account of how one fauna gives rise to the next.