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Rh considerable rainfall during the second period in most years. The only exceptions are rivers which have their' sources amongst mountains clad with perpetual snow, and are fed by glaciers; their floods occur in the summer from the melting of the snows and ice, as exemplified by the Rhone above the Lake of Geneva, and the Arve which joins it below. But even these rivers are liable to have their flow modified by the influx of tributaries subject to different conditions, so that the Rhone below Lyons has a more uniform discharge than most rivers, as the summer floods of the Arve are counteracted to a great extent by the low stage of the Saône flowing into the Rhone at Lyons, which has its floods in the winter when the Arve on the contrary is low.

Transportation of Materials by Rivers.—Another serious obstacle encountered in the improvement of rivers consists in the large quantity of detritus brought down by them in flood-time, derived mainly from the disintegration of the surface-layers of the hills and slopes in the upper parts of the valleys by glaciers, frost and rain. The power of a current to transport materials varies with its velocity, so that torrents with a rapid fall near the sources of rivers can carry down rocks, boulders and large stones, which are by degrees ground by attrition in their onward course into shingle, gravel, sand and silt, simultaneously with the gradual reduction in fall, and, consequently, in the transporting force of the current. Accordingly, under ordinary conditions, most of the materials brought down from the high lands by the torrential water-courses are carried forward by the main river to the sea, or partially strewn over flat alluvial plains during floods; and the size of the materials forming the bed of the river or borne along by the stream is gradually reduced on proceeding seawards, so that in the Po, for instance, pebbles and gravel are found for about 140 m. below Turin, sand along the next 100 m., and silt and mud in the last 110 m. When, however, the fall is largely and abruptly reduced, as in the case of rivers emerging straight from mountainous slopes upon flat plains, deposit necessarily occurs, from the materials being either too large or too great in volume to be borne along by the enfeebled current; and if the impeded river is unable to spread this detritus over the plains, its bed becomes raised by deposit, causing the river in flood-time to rise to a higher level. The materials, moreover, which are carried in suspension or rolled along the bed of the river to the sea, tend to deposit when the flow of the river slackens and is finally brought to rest on encountering the great inert mass of the sea, especially in the absence of a tide and any littoral current, and this is the cause of the formation of deltas with their shallow outlets, barring the approach to many large rivers.

Influence of Lakes on Rivers.—Sometimes a peculiar depression along part of a valley, with a rocky barrier at its lower end, causes the formation of a lake in the course of the river flowing down the valley. The intervention of a lake makes the river, on entering at the upper end, deposit all the materials with which it is charged in the still waters of the lake; and it issues at the lower end as a perfectly clear stream, which has also a very regular discharge, as its floods, in flowing into the lake, are spread over a large surface, and so produce only a very slight raising of the level. This effect is illustrated by the river Rhone, which enters the Lake of Geneva as a very turbid, torrential, glacier stream, and emerges at Geneva as a sparkling, limpid river with a very uniform flow, though in this particular case the improvement is not long maintained, owing to the confluence a short distance below Geneva of the large, rapid, glacial river, the Arve.

The influence of lakes on rivers is, indeed, wholly beneficial, in consequence of the removal of their burden of detritus and the regulation of their flow. Thus the Neva, conveying the outflow from Lake Ladoga to the Baltic, is relieved by the lake from the detritus brought down by the rivers flowing into the lake; and the Swine outlet channel of the Oder into the Baltic is freed from sediment by the river having to pass through the Stettiner Haff before reaching its mouth. The St Lawrence, again, deriving most of its supply from the chain of Great Lakes of North America, possesses a very uniform flow.

River Channels.—The discharge of the rainfall erodes the beds of rivers along the lowest parts of the valleys; but floods occur too intermittently to form and maintain a channel large enough to contain the flow. A river channel, indeed, generally suffices approximately to carry off the average flow of the river, which, whilst comprising considerable fluctuations in volume, furnishes a sufficiently constant erosive action to maintain a fairly regular channel; though rivers having soft beds and carrying down sediment erode their beds during floods and deposit alluvium in dry weather. As the velocity of a stream increases with its fall, the size of a channel conveying a definite average flow varies inversely with the fall, and the depth inversely with the width. A river channel, accordingly, often presents considerable irregularities in section, forming shallow rapids when the river flows over a rocky barrier with a considerable fall, and consisting of a succession of pools and shoals when the bed varies in compactness and there are differences in width, or when the river flows round a succession of bends along opposite banks alternately.

A river flowing through a flat alluvial plain has its current very readily deflected by any chance obstruction or by any difference in hardness of the banks, and generally follows a winding course, which tends to be intensified by the erosion of the concave banks in the bends from the current impinging against them in altering its direction round the curves. Sometimes also a large river, bringing down a considerable amount of detritus, shifts its course from time to time, owing to the obstruction produced by banks of deposit, as exemplified by the Po in traversing the portion of the Lombardy plains between Casale and the confluence of the Ticino.

Floods of Rivers.—The rise of rivers in flood-time depends not merely on the amount of the rainfall, but also on its distribution and the nature of the strata on which it falls. The upper hilly part of a river basin consists generally of impermeable strata, sometimes almost bare of vegetation; and the rain flowing quickly down the impervious, sloping ground into the water-courses and tributaries feeding the main river produces rapidly rising and high floods in these streams, which soon pass down on the cessation of the rain. The river Marne, draining an impermeable part of the Upper Seine basin, is subject to these sudden torrential floods in the cold season, as illustrated by a diagram of the variations in height of the river at St Dizier from November to March 1903-4 (fig. 2). On the contrary, rain falling on permeable strata takes longer in reaching the rivers; and the floods of these rivers rise more gradually, are less high, continue longer and subside more slowly than in rivers draining impervious strata, as indicated by the diagram of the Little Seine at Nogent during the same period, which has a permeable basin (fig. 1). A main river fed by several tributaries, some from impermeable and others from permeable strata, experiences floods of a mixed character, as shown by the diagram of the same floods in 1903-4 of the Seine at Paris, below the confluence of the torrential Marne and Yonne, where the floods of the gently flowing Upper Seine and other tributaries with permeable basins also contribute to the rise of the river (fig. 3).

High floods are caused by a heavy rainfall on land already sodden by recent rains at a period of the year when evaporation is inactive, and especially by rain falling on melting snow. A fairly simultaneous rainfall over the greater part of a moderate sized river basin is a tolerably common occurrence; and under such conditions, the floods coming from the torrential tributaries reach their maximum height and begin to subside before the floods from the gently flowing tributaries attain their greatest rise. Exceptional floods, accordingly, only occur in a main river when a heavy rainfall takes place at such periods over different parts of the basin that the floods of the various tributaries coincide approximately in attaining their maximum at certain points in the main river.

Mitigation of Floods and Protection from Inundations.—As the size of the channel of a river is generally quite inadequate to carry down the discharge of floods, the river overflows its