Alpine rocks, in the Valais along the Rhône, in the Tyrol along the Inn and Adige, in the Grisons, and in the Jura along the Rhine. Where the lines of stratification are horizontal, rivers usually take their course through the most marked ravines and fissures.

In most mountains, however, the lines of stratification are neither vertical nor horizontal, but intermediate between them, more or less sloping, as in most marked ranges of central Germany, for example. In such cases, the process of excavating river-beds has been determined by various circumstances and conditions, and the direction of their channels does not depend alone upon the extent and tilt of the strata, but also on other forces which have exercised a favouring or a retarding influence on their direct course. The stratification has its influence, indeed, but it is general rather than specific. Still, it is very largely felt when it happens to coincide in its main lines with the direction of the mountain-range, but is comparatively insignificant when it does not. We have instances in the Alps where the axis of stratification coincides with that of the main chain, from south-south-west to northnorth-east; in the Jura, from south-west to north-east; and in the Scandinavian range, from south to north.

The different geological formations found in mountain districts have a very important influence in determining the direction of rivers. Mountains do not generally consist of rocks of one kind of structure, but of several. What stratification is to mountains whose geological formation is the same throughout, the superposition of different kinds of rocks is to those of composite materials. The layers may be divided into superior, inferior, and adjacent. These usually vary in respect to age, and may be traced in a regular geological seniority, as, for example,

sandstone, gypsum, limestone, greywacke, and granite. These formations are either closely contiguous, or are separated merely by valleys,-as, for instance, in the Carpathian chain, where the central granite knot is separated by valley plains from the more southern limestone chain; an example of contiguity is found on the west spur of the same Carpathian range. Wherever mountain-systems of varied geological structure approach each other very closely, rivers seldom break through either, but find their way along the roots of the mountains, till at last they come to a less confined place. Such river-courses are often very large and deep; for the mountain streams which meet and are hemmed in by the narrow pass between the two contiguous ranges sweep all loose obstructions before them, and not only leave their path clear, but continually deepen it. We find this in the Ural, the Isère, the Rhône, Aar, Inn, in all the long and winding Alpine valleys, and in the Ebro, fed by the parallel ridges of the Pyrenees. The circle of rivers which girds the central Carpathian knot is an illustration of what was said a moment since. The Poprad, Dunajec, Arva, and Waag are found where the true Carpathian chain, which is granitic, is closely contiguous to subordinate ranges of limestone and greywacke. In any accurate map the long winding course between these two chains may be easily traced. Looking at the point where the Hartz Mountains and the Thuringian ridge touch at their roots, the groups are seen to be insulated, as it were, by the rivers which gird their bases. In the great streams of southern and south-western Asia, too, the line of the water-courses can be traced along the narrow valleys which separate main from subordinate mountain-chains; the Terek, Kuban, Kur, 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 portions-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 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 great, that an almost infinite diversity ensues in the characteristics of rivers; and these characteristics always vary, too, according as they are found in the upper, middle, or lower course.

UPPER COURSE OF RIVERS.

This begins at the ridge of the watershed, and extends to the limits where the river emerges from the 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 neighbourhood. The farther they advance from the watershed the more they recede 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 portage, the English word transport being little used in that connection, although all, the German Trageplätze 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 watershed-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 forming canals 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 watershed 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. The grade of most mountains' sides, which stand back to back, is unlike on the two sides steep on the one, gradual 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 Carpathian and the Alps, just the

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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 6°, taking the entire upper course into account. On the very steep north side of the Pyrenees, the fall is between 3° 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 33°. 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 meadow-like 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 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