Darwin's Explanation of the Origin of Coral Reefs

It's Darwin's explanation of the origin of coral reefs (and it was Nick Humphrey who told me this story in the early 1980's—in Tahiti!). What I love is that the question is so easy to grasp but so difficult to answer, and that Darwin's solution is so simple and beautiful—he worked it out by sheer power of imaginative reasoning long before anybody had heard of tectonic plates and more than a hundred years before the theory would be proved (by deep borings on Bikini Atoll).

The mystery, much discussed in the 1830's, was that coral polyps can grow and reproduce only in shallow water, and yet the walls of coral reefs and atolls plunge thousands of feet into the deep ocean. The coral couldn't have grown from the bottom upwards, so how then did the reef and atolls get there? 

By the 1830's, the geologist Charles Lyell had decided that atolls must be coral reefs growing on the crater rims of sunken extinct volcanoes. Darwin didn't agree, and it's wonderful to know that Lyell was thrilled when Darwin came back from the Beagle voyage and told him the real answer: the coral organisms thrive in shallow water but the ocean floor is slowly sinking; the polyps die but new ones are growing on top of them, and over an immense amount of time countless billions of tiny calcareous skeletons accumulate to make up a vast structure reaching from the darkness of the ocean bed to the sunlit surface so far above.