THE HYDRAULICS OF GREAT RIVERS. 329 



of the Parana Guayaza, where the river is about three-lburths 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. Revy, which constitutes the largest measurement of a river sec- 

 tion 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 aver- 

 age depth w^as 47^ feet, and the greatest 72 feet, w^hile 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. Revy'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 inclina- 

 tion 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 fric- 

 tion 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 satisfacto- 

 rily done before. Many experiments, with a view to the accomplish- 

 ment 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. Revy has established that 

 the velocity of a river is directly proportionate to its depth, diminish- 

 ing 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- 



