The proportionate increase of the structures, according to Mr. Darwin, depends at once upon the species which construct the reefs and upon various accessary circumstances. The ordinary rate of increase of the madrepores, according to Dana, is about an inch and a half annually; and, as their branches are much scattered, this will not exceed half an inch in thickness of the whole surface covered by the madrepore. Again, in consequence of their porosity, this quantity will be reduced to three-eighths of an inch of compact matter. It is, besides, to be noted that great spaces are wanting; the sands filling up the destroyed part of the polyp are washed out by the currents in the great depths where there are no living corals, and the surface occupied by them is reduced to a sixth of the whole coralline region, which reduces the preceding three-eighths to one-sixth. The shells and other organic débris will probably represent a fourth of the total produce in relation to corals. In this manner, taking everything into account, the mean increase of a reef cannot exceed the eighth of an inch annually. According to this calculation, some reefs which are not less than two thousand feet thick would require for their formation a hundred and ninety-two thousand years. It is necessary to add, however, that in favourable circumstances the increase of the masses of coral may be much more rapid. Mr. Darwin speaks of a ship which, having been wrecked in the Persian Gulf, was found, after being submerged only twenty months, to be covered with a bed of coral two feet in thickness; he also mentions experiments made by Mr. Allen on the coast of Madagascar, which tend to prove that in the space of six months certain corals increased nearly three feet. * * * * * We proceed to the theoretic explanation of these curious mineral formations.