The proportions in the length of the upper, middle, and lower course of rivers are exceedingly variable; and equally variable of course are the transition lands apportioned to each, and forming its natural supplement. The upper course of the Volga is very short, the middle very long, and the lower very short. The same relative proportions, though with very different dimensions, are found in the Vistula, the Ganges, the Euphrates, and the Mississippi. The upper course of the Rhine, on the contrary, is very long, through all Switzerland to Bâle; the middle also very long, to Cologne; the lower, very short, to Rotterdam and the sea. It is the same with the Nile, the Danube, and the Indus. In the Marañon or Amazon the upper course is very short, the middle and lower very long. In the Chinese rivers Hoang-ho and Yang-tse-Kiang all the three courses are relatively long. The length of the middle and lower courses, although important conditions of navigation, are not the only ones. Others are not to be overlooked,—the amount of water, depth of channel, and the like. These, however, are not capable of being generalized under any law, but depend upon the individual characteristics of each stream. Every river needs, for an exhaustive account of its features, its own monograph. There remains but one important point to be considered—one which has exerted a very great influence on the diversity of structure in all river systems, controlling the area of their drainage, their volume of water, their effect on human culture, and on the ethnographic character of the people dwelling on their banks. It is the distance from the source to the mouth in direct distance compared with that following the tortuous course of the stream. The two lines almost never coincide; they generally lie far apart. And the less they approach to coincidence, the greater becomes the area of the river basin; the more numerous and valuable the tributaries to the main course, the greater the volume of the stream and the more varied and extensive its influence. One or two examples drawn from European rivers will more fully explain this point, to which Buache has already called attention in his “Parallèle des fleuves.”