22 Rema7-ks on the Formation of Alluvial Deposites. 



lotti, one of the Italians, maintained, that " the velocities of 

 streams increase nearly as the square roots of their depths," and 

 this is admitted by Professor Robison, who embraces the new 

 theory. Du Buat, on whose authority the new theory princi- 

 pally rests, maintains, that, " as the depth increases, the velo- 

 city at the bottom of the stream increases even in a higher ratio 

 than the velocity at the top," and this is also the opinion of Pro- 

 fessor Robison*. The opponents of the old theory, Avho say 

 that the velocity is the essential circumstance to be considered, 

 must therefore allow, that an increase of depth in any stream 

 produces an increase of power to carry heavy substances at the 

 bottom, and this is all that is necessary for my present purpose. 



The effect of increased depth, in augmenting the force at the 

 bottom of a stream, is evident in the case of water discharged 

 froxTi any opening. Whether the water flow through artificial 

 spouts and conduits, or over natural channels of rock, we ob- 

 serve that it is emitted with a force proportioned to its depth. 

 If the current be very low, it moves so sluggishly, that it does 

 not overcome the adhesion of its under surface to the surface of 

 its channel, and hence it discharges itself by trickHng over the 

 edge, and will even move some distance back^vards, if the edge 

 overhangs. If, by an addition to the quantity of water, or in 

 any other way, its depth be augmented, the current will dis- 

 charge itself more freely and perpendicularly ; and, on a still 

 further increase, it will quite overcome the adhesion to its chan- 

 nel, and will fly off from it in a curve. 



In this inquiry I leave out of view the inclination of the bed, 

 because it is my object to account for the distribution of allu- 

 vium over extensive tracts, which either have no inclination, or 

 none which is sufficient to account for the appearances. In any 

 case where there is a perceptible declivity, as in torrents, rapids, 

 and waterfalls, it is manifest, that the velocity of the water, and 

 of the earth and stones contained in it, is increased, because they 

 are urged to fall, not only by the force impressed, but by their 

 own weight. Nevertheless, the quantity of direct vertical mo- 

 tion thus acquired, is destroyed almost immediately by their im- 

 pinging upon various obstacles, so that, if we look at the water 



>i't fltlW 

 ^ See End. Brit. Art. Rivers, sect. 71 & 77. 



