of the Paraná Guayaza, where the river is about three-fourths of a mile wide, is 12 feet, and that the flood-level is always maintained for three months. The river occasionally rises to 24 feet above the low-water line, but this is rare, and its low-water supply never falls below half the volume of the ordinary flood. At a point near Rosario, where the river is 4,787 feet wide, a series of measurements has been made by M. Révy, which constitutes the largest measurement of a river section yet effected. "The depth increases by a gentle and regular slope, from that of a few inches, on the left shore, to 72 feet, at a distance of about 1,100 feet from the right bank. Thence it rapidly shallows to about 12 feet, and then rises gradually to the foot of a vertical cliff, forming the right-hand shore of the river." These measurements were made in January, when the river was at low water. The average depth was 471⁄2 feet, and the greatest 72 feet, while the sectional area measured 184,858 feet. The same section, during the ordinary flood, gives a measurement of 243,000 feet, or a little less than one-third greater. This, however, does not give an adequate idea of the increase in volume, as, at the height of the flood, the left bank of the river is submerged for many miles. The flow, independent of the escape over the marshes, is estimated, according to M. Révy's data, as 40,000,000 metric tons per hour at low water, 83,000,000 at the ordinary flood, and 169,000,000 at the occasional extraordinary floods.
The velocity of a river depends upon the inclination or fall of its course, and its surface velocity can be ascertained by determining the rate of that fall per mile, and vice versa we can ascertain the inclination by measurement of the surface velocity. But, as every one who has stirred up the bottom of a brook has observed, the surface-current flows faster than the under-current. The particles of sand at the top of the water are always carried some distance beyond those at the bottom. This retardation of the under-current is caused by the friction of the water against the bottom and sides of the brook. While therefore, it is easy to measure the velocity of the surface-current, it is difficult, because of this retardation beneath, to determine the mean velocity or actual flow of the river. This has never been satisfactorily done before. Many experiments, with a view to the accomplishment of this end, have indeed been made by eminent men, but they have failed to establish the relationship between the depth of the stream and the velocity of the flow. M. Révy has established that the velocity of a river is directly proportionate to its depth, diminishing or increasing therewith. "Thus if a shoal occurs in the middle of a channel, the velocity of the current over the shoal is less than that of the deeper water on either side; and this diminution of speed is proportionate to the loss of depth. So direct is this relation, that a plan of the surface velocities, if projected on an appropriate scale, coincides very closely with the section of the bottom of the river. Any want of parallelism between the two curves is capable of expla-