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Every schoolchild sooner or later learns the standard story of the origins of oil; it runs something like this. Once upon a time, hundreds of millions of years ago, the earth was covered by vast oceans. Animals, plants and micro-organisms in the seas lived and died by the billion, their remains sinking to the bottom and mixing with sand and mud to form marine sediment. As the ages passed, the mud turned to rock and eventually the organic mass became buried deep under layers of rock. The oceans receded and the earth's crust heaved and buckled. Compressed under this vast weight of rock, decomposition occurred and the layers of biomass underwent a chemical change to form hydrocarbons (compounds composed only of hydrogen and carbon atoms) – coal, oil, and natural gas.
Special geological conditions are needed to keep the oil trapped underground. The organic material has to be covered by porous rocks and these, in turn, have to be covered by an impermeable layer which acts as a cap to prevent the oil and gas escaping. Oil is consequently found only in places where these geological conditions are met.
This is the most celebrated chapter of the book and it has been widely commented upon in biological literature. I have not made any careful survey, but I suspect that the well-known diagrams of transformations have been reproduced in sundry scientific writings a large number of times.
The comments almost invariably have a few points in common, which I shall briefly summarise here. In the first place it is surprising that despite their fame, the Cartesian transformations have been used very little. This is because, to use Medawar's term, they are ‘analytically unwieldy’. The few times the method has been applied is in the development or change of form in a single system, as for instance, Richards and Riley's study of developing amphibians under different conditions, and Medawar's analysis of tissue culture growth.
A far more significant result in terms of practical application is that the system of transformations of D'Arcy Thompson stimulated and contributed to the much simpler method of analysis of allometric growth, which has found widespread use, mainly through the work of J. S. Huxley. Here instead of attempting to analyse a whole structure in two (or three) divisions, two factors are isolated and compared on a logarithmic scale. In this way it is possible to discover the ratio of the growth-rates of different structures, a method which has found application in embryology, taxonomy, palaeontology and even ecology.