The division of the whole length of a river into the three courses—the upper, middle, and lower—and the proportionate share which each of these bears to the whole, depends upon the height at which the source stands above the mouth. The greater or less extent of the transition grades, and the greater or less extent of navigable waters, also depend on the same. The upper course has, as a general rule, too many hinderances to be very valuable for navigation; it is, at best, adapted only to boats. The more united and deeper middle course offers facilities for vessels of considerable draught; yet the frequent sunken rocks and eddies and rapids are a great impediment to navigation. We find it so in the Rhine, below the Falls of Schaffhausen, as far as Bâle; and in its middle course, at Bingen and St. Goar; in the Danube, also, at Grein and Orsova.

The lower course, on the other hand, opens like a broad fresh-water sea, that sometimes allows large ships to sail 50, 200, and even 500 miles inland. These maritime streams ought to be discriminated from others; the Chinese call them “sons of the ocean.”

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.”

The mouth of the Volga is 982 miles distant from the source, in an air-line. The distance, including all the curves of the stream, is 2012 miles, the bendings adding 1028 miles to the direct course. By this doubling of the shortest possible distance, the area drained by it is swollen to the enormous size of 657,000 square miles. The direct course lies in a diagonal direction from northwest to southeast; but the real direction is a changing one. First, it flows a short distance from north to south, then in its middle course it has a double direction; first eastward, toward the Ural chain, then to the south, and lastly, in its lower course, to the southeast. Through this varied course it receives tributaries from very remote sources, and waters a country altogether greater than would be possible if the Volga’s course were direct from the source to the mouth. Its basin becomes so large as to embrace a fifth of Europe, and the stream becomes one of the longest and most available for navigation in the continent. The vastness of the volume of water and the wandering course have both contributed to the value of the Volga lowlands.

The exact contrast to the Volga is found in the Dniester. In the Volga there is a maximum of windings; in the Dniester there is a minimum. The air-line distance of the mouth of the Dniester from the source is 408 miles; the distance, including all the bends, is 450 miles; the loss in winding is, therefore, but about 42 miles. The theoretical course of the Dniester, i.e. measured by an air-line, would coincide very nearly with its actual course. There cannot be, therefore, any distant springs whose waters flow into its channel; its basin is one of the most contracted in the world in consequence of its directness; and a small belt, embracing but 32,850 square miles, comprehends the entire district that it drains, freed from all those tributaries which make the Volga basin so important.

The Dnieper, its eastern neighbor, is 630 miles in direct distance from the source to the mouth, but 1000 with all its windings; leaving 370 miles as the extraneous shore, which adds to the value of the basin, and contributes to the 219,000 square miles which it drains.

The same contrast is seen elsewhere, though not on so extended a scale. It is to be found in the Vistula, Oder, Elbe, Weser, Rhine, and Danube. These rivers give shape to the transition terraces between broad eastern Europe and the more contracted western portions of the continent; their dimensions are, therefore, on a less extensive scale than in the great Russian streams. Still, the differences in them are worthy of notice.