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Asia, too, the line of the water-courses can be traced along the narrow valleys which separate main from subordinate mountain chains; the Terek, Kooban, Koor, Aras, Euphrates, Tigris, Indus, Ganges, and probably the Chinese rivers, are all examples of this.

Some streams seem to be entirely independent of all these laws in forming their channels, and to have their direction assigned to them by the freaks of nature, such, for instance, as fissures in mountain chains and clefts, which remain to indicate ancient convulsions.

The entire course of a river is divided into three distinct and subordinate courses-the upper, middle, and lower. To these and their respective tributaries correspond the three grades of transition found on the banks, and which have already been alluded to. Not only the total amount of fall in the river bed, but also the angle of inclination, and the whole complex of phenomena in the basin, are reciprocal to the threefold character of transition in almost every hydrographical system in the world. Still, the variety of relations which arise from the combination of different elements is so variable, that an almost infinite diversity arises in the characteristics of rivers, and these characteristics always vary, too, according as found in the upper, middle, or lower course.

Upper Course of Rivers.

This begins at the ridge of the water-shed, and extends to the limits where the river emerges from the most rocky highlands. It depends for its existence upon the greater fall in the river bed there than lower down. At the upper course, therefore, rivers which may flow in exactly opposite directions are brought into direct neighborhood. The farther they advance from the water-shed the more they re

cede from each other. In the High Forest south of the Carpathian chain, and in the Bory Morass north of it, the waters which flow into the Baltic and into the Black Seas spring from the ground side by side. The name given to the districts where the head-waters of large and navigable rivers part is usually the French word portages, the English word transports being little used in that connection, although all, the German Trageplatze and the Russian Wolok, involve the idea of carrying, of porterage, from the head-waters of one stream to those of another. The lowest parts of a water-shed, the passes of a high mountain range, for example, the intermediate vales of lower ones, and the most elevated plains in flat districts, are the most suitable for the purpose of canal building, to serve as a connecting link between the sources of divergent streams; as, for instance, the canal which is proposed to connect the Baltic and the Black Seas by uniting the Vistula and Danube, the tributaries, the Poprad, Hernad, and Theiss being the channel of communication up to the mountains where a canal is to pass over the water-shed formed by the valleys of the Carpathian chain. Such a communication is the most available which can be made between the opposite sides of a mountain range. The practicability of constructing such canals depends very largely upon the degree of fall in the upper course of the connected rivers, as determined by the slope of the bed toward the horizon. The grade of most mountains' sides, which stand back to back, is unlike on the two sides: steep on the one, slight on the other. Upon this depends the greater or less wildness of the streams flowing through their upper course. In the Ural chain the slope is steep on the eastern side, gradual on the western; in the Caucasus, steep on the north, gradual on the south; in the Carpa

thian and the Alps, just the reverse-steep on the south, gradual on the north. The rate of fall varies; but, in general, it lies between an angle of 2° and an angle of 6o, taking the entire upper course into account. On the very steep north side of the Pyrenees, the fall is between 3o and 4°; on the south side of the Alps, from the summits of Mont Rosa and Mont Blanc to the plains of Piedmont, it is 320. It is far less in more unimportant ranges. And this angle, it should be remarked, is an average; it is the resultant of a great number of special, short slopes, which vary from the perpendicularity of an occasional waterfall to the equally occasional tranquillity of a meadowlike flow. The incidental slopes are, of course, much greater than the average of all. A grade of 15° is very steep; it is the maximum that can be ascended by a beast of burden. A grade of 8° is the maximum for wheeled vehicles; all roads must be less sloping than this. To accomplish the ascent of 35°, a man on foot must have some assistance. A grade of 44° in the high peaks of Mexico and Peru, Humboldt found inaccessible; only where the growth of trees and shrubs gave him an opportunity of planting his feet, could he climb where it was a little steeper than 44°. The Carpathians and the Pyrenees, on account of their steepness and their scanty verdure, are very difficult to ascend. The Alps are much more easily climbed than the mountains just mentioned, in consequence of their abundant growth of turf and undergrowth. The richest Alpine meadows of Switzerland have an inclination not exceeding 20°; at a greater slope the vegetation becomes more sparse. The grade on which it is possible for earth to cling, Lehman fixes at 45°, and considers that the normal slope, because at a greater angle, rain glances or ricochets. But Lehman is not right in

assigning this as the normal slope possible for earth to cling and vegetation to grow, for on the Alps soil adheres and plants get a footing at a much steeper angie than 15°; in fact, the modifications in the appearance of the Alps, by the growth of trees clinging to steeper slopes than this, are very marked. From the highest possible grade where vegetation can get a footing, we advance to the sheer perpendicular.

The upper course of rivers is characterized rather by plunges than by equable flowing, and determines its way by a series of leaps through zigzag cuts and various ravines. It traverses bowl-shaped hollows and narrow defiles, and makes its way even through mountain lakes, depositing in them its residuum of sand and gravel which it has caught up and swept along. In its wild plu ges it draws into its body considerable air, which appears as bubbles, and makes it a white mass of foam. By-and-by it reaches more level ground, becomes clear as crystal, and assumes a rich emerald green, or a deep blue. It is unnavigable, wild, romantic, and is always found in mountain districts.

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The brawling brooks of Salzburg, of the Pyrenees, and of Sweden and Norway, all partake of this character. Those of the Pyrenees have a fall of an inch in every foot, and in some places cataracts of two or three feet. The same is observable in the Alps, where the continual stir of the water mixes in air enough to turn all into a mass of silvery-white foam. The Carpathian waters are the same before they reach the high plateaus lying at their feet. The Alpine lakes, too, which lie within the upper course of the rivers which feed them, have a considerable fall; Lago Maggiore, for instance, has a descent of 52 feet between Magadino and Arona.

In all the most marked mountain systems of Europe, the upper course of the rivers is especially prominent. Northern Europe is characterized by the fact that its streams have, throughout the most of their length, the peculiarities of the upper course-whether observed in northern Russia, in all Sweden, Norway, and Scotland.

With the exit of the river from the mountain district, all these relations are changed, and a new character begins.

The Middle Course.

Far more moderate is the descent after the river emerges from the mountain region, or where it has never experienced the wild turbulence of the upper course, as is the case in most of the rivers of eastern Europe. In the middle course the angle of inclination is much modified. The upper Main has a fall of 342 feet within three miles after leaving Fichtel Mountains. The descent of most of the rivers of central Germany is much less than this. The Neckar, whose sources lie 2084 feet above the sea, in passing to Heilbronn, which is 450 feet above the sea, falls at the rate of about an inch to every 32 feet. The fall of the Saale, after leaving the Fichtel range, is about 20 feet to the mile; that of Naab, about 14; that of the Eger, less; and that of the upper Oder, in Silesia, still less. More gradual yet is the slope of the Volga bed, which falls but 1400 in about 2050 miles, considerably less than a foot to a mile; and in its lower course its inclination must be still less.

The effects of the current must necessarily be very different from those observable under the influence of the dashing and wayward upper course.

The name River Bed is given to the entire breadth of the hollow which holds the river, and which varies in

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