Some few even among coral-polyps live individual lives, but the greater number follow the community-system. This must always be looked upon as an inferior way of existence. The most usual way in which polyps increase is by “budding”--not unlike the growth of a plant by buds. A small lump appears on one side of the parent, which increases fast in size, develops a mouth and tentacles, and by-and-by gives birth itself to other buds. The increase of numbers is enormous. One polyp may produce in a short time thousands or even tens of thousands of descendants. But in the case of coral-polyps the children do not leave the parents or go out into the world. They cling to the old stock; they partake of the united family-life; and each little mouth and stomach works for the benefit of all the little stomachs of the whole community. Some polyps, instead of budding like a plant, increase by division. One polyp separates into two parts, each of which becomes a full-grown animal; and each then divides anew; this plan continuing _ad infinitum_. Here again the growth of numbers is not slow. Occasionally, in place of spreading in branch-like shapes, they grow in solid rounded masses. Such a sphere-like mass in tropical waters of the Pacific may be twenty feet in diameter--one huge family of united beings, each perhaps under a twentieth of an inch across, and all together clothing a skeleton common to the entire clan. In these cases the tips of the branches or the outer edges of the rounded mass are the _young_ polyps, while the older ones lie lower down or more inward. As the tree or ball of coral grows, spreading farther, giving birth to fresh generations of polyps, the old ones die off. So the living and the dead are found in one community, in close touch, on a single branch or a single mound of coral. At the tip of each twig may be the brightly-coloured active jelly, while the stem below is a dead skeleton. On a solid mass of coral, twenty feet in diameter, the whole outside may be alive, down perhaps to a depth of half-an-inch, while the whole inside is lifeless bone. That is how the coral grows. Living coral is seldom found at any greater depth in the sea than about twenty fathoms, and the limits of temperature which the polyps can endure are narrow. Their growth is quickly checked by water a little too deep or a little too cold, and by water not very pure. Abundance of lime also is needful. An “atoll” is a coral-reef standing alone, generally of a round or oval shape, with a lake of calm sea-water in its centre, while ocean-billows thunder on the outer margin. The polyps love those waves; but they fade and die in the inclosed lagoon, where the water is not often enough renewed to supply them with food. Much the same in make are the Fringing Reefs and Barrier Reefs, except that the former skirt the shore more closely, while the latter may lie at a distance of many miles from island or mainland.