The application of the Cartesian coordinates to the outline of organisms, skulls, bones, and organs of animals has opened up a new field of mathematics--biological research which has yielded many results confirming theories based on other data and supplying facts of great interest that may at any time result in the establishment of important generalizations. The fact of beauty in animate nature is so pronounced, and man's contemplative delight in beautiful things is so natural that investigations have been made into the æsthetic emotions of other animals. A vast array of facts has been collected which leaves no doubt of the universal appreciation of beauty. The lovely colors of shells, butterflies and birds, the extraordinary beauty of the designs of the frames of the Foraminifera, radiolarians and sponges, the graceful logarithmic spirals of horns and flower and leaf buds, and the charming flowing lines in the shape of the race horse and gazelle, these elements of organic beauty which emphasize and enhance the forms of animals, all contribute to the general embellishment of nature. The combinations of beauty of form, color, and movements in parrots, humming birds, the fish inhabiting coral reefs, butterflies, and orchids, are always perfect. We likewise find that in all parts of the globe, and in each life zone, organic beauty conforms to that of the landscape and the heavens. The biological significance of this universality of beauty in the organic world will be dealt with in the following chapter. The fishes of the seas, rivers, streams, and lakes have been studied, classified, and described as completely as the insects of the air, the field, the soil, and those parasitic upon other organisms. The surveys of the Atlantic have brought to light many types of fish which inhabit only the deepest parts of the ocean. These fish are modified in most extraordinary ways to fit their surroundings. Owing to the darkness of their living zones, they are provided with luminescent appendages which are practically similar to the firefly's and glowworm's electric generators. The lights are formed, as in the insects, by the oxidation of material exuded by the fish. There are more than 180 families of fishes recorded. Each family contains an average of twenty genera and each genus about five species. The known species of fish are, therefore, between 19,000 and 20,000. The Danish naturalist Hensen found 278,795,000,000 fecundated fish eggs per square mile in the summer waters of the Skagerrack. The waters of the seas from the Arctic to the Antarctic limits are full of fish eggs as well as those of shellfish and sea organisms generally. This shows that organic life is as abundant in the sea as anywhere on land. Just as temperature and salinity are the chief agents of oceanic circulation and current movements, so they are the leading factors in promoting the organic life of the sea.