I will begin this inquiry with a series of facts which I myself have had an opportunity of investigating with especial care respecting the formation and growth of the Coral Reefs of Florida.  But first a few words on Coral Reefs in general.  They are living limestone walls that are built up from certain depths in the ocean by the natural growth of a variety of animals, but limited by the level of high-water, beyond which they cannot rise, since the little beings that compose them die as soon as they are removed from the vitalizing influence of the pure sea-water.  These walls have a variety of outlines:  they may be straight, circular, semicircular, oblong, according to the form of the coast along which the little Reef-Builders establish themselves; and their height is, of course, determined by the depth of the bottom on which they rest.  If they settle about an island on all sides of which the conditions for their growth are equally favorable, they will raise a wall all around it, thus encircling it with a ring of Coral growth.  The Athols in the Pacific Ocean, those circular islands inclosing sometimes a fresh-water lake in mid-ocean, are Coral walls of this kind, that have formed a ring around a central island.  This is easily understood, if we remember that the bottom of the Pacific Ocean is by no means a stable foundation for such a structure.  On the contrary, over a certain area, which has already been surveyed with some accuracy by Professor Dana, during the United States Exploring Expedition, it is subsiding; and if an island upon which the Reef-Builders have established themselves be situated in that area of subsidence, it will, of course, sink with the floor on which it rests, carrying down also the Coral wall to a greater depth in the sea.  In such instances, if the rate of subsidence be more rapid than the rate of growth in the Corals, the island and the wall itself will disappear beneath the ocean.  But whenever, on the contrary, the rate of increase in the wall is greater than that of subsidence in the island, while the latter gradually sinks below the surface, the former rises in proportion, and by the time it has completed its growth the central island has vanished, and there remains only a ring of Coral Reef, with here and there a break, perhaps, at some spot where the more prosperous growth of the Corals has been checked.  If, however, as sometimes happens, there is no such break, and the wall is perfectly uninterrupted, the sheet of sea-water so inclosed may be changed to fresh water by the rains that are poured into it.  Such a water-basin will remain salt, it is true, in its lower part, and the fact that it is affected by the rise and fall of the tides shows that it is not entirely secluded from communication with the ocean outside; but the salt water, being heavier, sinks, while the lighter rain-water remains above, and it is to all appearance actually changed into a fresh-water lake.