It would indeed be a great mistake to suppose that rivers always tend to deepen their valleys. This is only the case when the slope exceeds a certain angle. When the fall is but slight they tend on the contrary to raise their beds by depositing sand and mud brought down from higher levels. Hence in the lower part of their course many of the most celebrated rivers--the Nile, the Po, the Mississippi, the Thames, etc.--run upon embankments, partly of their own creation. [Illustration: Fig. 48.--Diagrammatic section of a valley (exaggerated) _R R_, rocky basis of valley; _A A_, sedimentary strata; _B_, ordinary level of river; _C_, flood level.] The Reno, the most dangerous of all the Apennine rivers, is in some places as much as 30 feet above the adjoining country. Rivers under such conditions, when not interfered with by Man, sooner or later break through their banks, and leaving their former bed, take a new course along the lowest part of their valley, which again they gradually raise above the rest. Hence, unless they are kept in their own channels by human agency, such rivers are continually changing their course. If we imagine a river running down a regularly inclined plane in a more or less straight line; any inequality or obstruction would produce an oscillation, which when once started would go on increasing until the force of gravity drawing the water in a straight line downwards equals that of the force tending to divert its course. Hence the radius of the curves will follow a regular law depending on the volume of water and the angle of inclination of the bed. If the fall is 10 feet per mile and the soil homogeneous, the curves would be so much extended that the course would appear almost straight. With a fall of 1 foot per mile the length of the curve is, according to Fergusson, about six times the width of the river, so that a river 1000 feet wide would oscillate once in 6000 feet. This is an important consideration, and much labour has been lost in trying to prevent rivers from following their natural law of oscillation. But rivers are very true to their own laws, and a change at any part is continued both upwards and downwards, so that a new oscillation in any place cuts its way through the whole plain of the river both above and below. The curves of the Mississippi are, for instance, for a considerable part of its course so regular that they are said to have been used by the Indians as a measure of distance.