Hydraulics of the Mississippi River. — 197 
Art. XVITI.— Hydraulics of the Report of Humphreys and Abbot 
on the Mississippi River; by Prof. F. A. P. BARNARD. (Con- 
tinued from p. 37.) 
For the solution of most problems in practical hydraulics, it 
is necessary to establish the relations which exist between the 
_ cross-section of the stream, its mean velocity, and the slope of 
its surface. As a basis of this investigation, it is assumed b 
equation presents no difficulty; it is simply the expression for 
the force of gravity. The other requires consideration. 
The authors of the report reject the idea that the cohesion of 
the particles of the liquid among themselves enters as an element 
into the resistance of the liquid to motion. ey hold that this 
cohesion is concerned only in determining the distribution of the 
resistance through the mass; but that the resistance itself is 
simply the adhesion of the liquid to its bed. It is unnecessary 
to stop just here to discuss the question by what name it is most 
fitting that the resistance to flowing water shall be called. It is 
quite sufficient, if we agree that were the resistances, irregulari- 
ties, and obstructions to motion, at the surfaces of contact be- 
tween the water and the earth or the superincumbent air, to be 
roportioned to the perinfeter and length of channel; and, also, 
use, when there is no motion, there is no resistance, to some 
function of the mean velocity at the surfaces in contact. Now, 
_ @=cross-section of the river, =width, 
p=wetted perimeter, r=="==mean radius, or hydraulic depth, 
_ Lelength of channel considered, A—=total head or difference of level, 
' hy=part of head balanced against ordinary resistances of the channel, 
h,=part of head neutralized by bends, and irregularities, 
