These are but approximations to the exact mathematical statement; but they serve to indicate comprehensively this important fact. No exact canon now exists for the perfect expression of the relations of the continents to each other, and their physical superiority and inferiority, and its lack is no less felt than it has been in art to express the comparative importance of the organs of the human body in giving a representation of man. The New World. America is broken by the Caribbean Sea into a double continent, both parts being of colossal magnitude, although the southern portion is about 2,000,000 square miles less in area than the northern. North America contains 9,055,146 square miles. South America contains 7,073,875 square miles; and both contain 16,129,021. The connecting link is found in the tapering isthmus of Central America, with its 302,443 square miles of surface. But closely connected as is the northern part of the continent with the southern, in a physical sense, in real connection, so far as man is concerned, they are widely separated. During the three centuries which have elapsed since the discovery of America, the Spanish and the Americans have thought of breaking the connection—of sundering the isthmus. All communication between North and South America takes place by water, absolutely none by land. Even before the navigation of the historical period, there seems to have been no land road opened along the isthmus. The old race of the Caribs passed in boats from the Appalachian mountain land of North America to South America and the West Indies. The Toltecs and Aztecs—the oldest tribes which wandered southward—seemed to have ended their march on the high plateau of Mexico and the vale of Anahuac. The legends of the Incas give us no tidings of their traversing the isthmus and reaching Peru on foot, and it is probable that they reached that land otherwise. The isthmus seems never to have been a bridge, but always a barrier. The great Antilles group of islands appears to have served far more as a means of communication between North and South America.