Report of Messrs. Humphreys and Abbot. a 
avoided. The laws which we are about to state, are, therefore, 
to be understood of waters moving uniformly in channels straight 
and regular. With this explanation, we cite from the report, i 
a form condensed from that in which we find them, the following 
ropositions :— 
3 In a uniformly flowing stream, the maximum velocity of the 
water, in any vertical plane parallel to the current, is not found 
at the surface, but at a point situated a little more than three 
tenths of the ‘depth below the surface. 
o whatever cause it may be owing, there is a resistance to 
the flow of water at the surface, similar in kiud to that which 
takes place at the bottom, though u usually less in degree. This 
resistance is propagated downward, according to a law of dimi- 
nution similar Me sr with which the resistance at the bottom is 
propagated u 
If the daaiien in the same vertical plane, parallel to the 
current, be plotted as ordinates, and the depths at which they 
are observed as abscissee, the curve drawn anise the points 
thus determined is sensibly a parabola, having the filament of 
maximum velocity for its axis, which is, of course, horizontal. 
This parabola varies its curvature with the changes in the 
mean velocity of the river; the curvature being at its maximum 
when the velocity is greatest. When the velocity is zero, the 
parabola becomes a straight line. 
The law which governs the curvature is determined by the 
proposition, that the reciprocal of the parameter of the parabola 
varies as the square root of the mean velocity of the river. The 
reciprocal of the parameter of sub-surface velocity is therefore 
the ordinate in another parabola, in which the mean velaeney: of 
the river is the abscissa. 
sates of the parabola of parameters is, for rivers 
, o« Phe 
E generally, s nsibly constant. It is, wanes er, a function of the 
nat 
such a 5 exainion that the variations are nearly inap- 
| eoroiable for river formulz, except for depths less than twenty 
or perhaps twelve feet, 
he variations of alosity 5 in horisoutal planes, at the surface 
or below it, follow the same law as in vertical planes, the curve 
which represents them being a parabola having its axis in the 
thread of maximum velocity. 
The depth of the axis of sub-surface velocities in vertical 
planes is affected by the wind, being depressed when the wind 
is up-stream, and elevated when the wind is down-stream, The 
amount of displacement is Hpi proportional to the force of 
the wind and the depth of the river, and is sensibly the same 
for the same wind-force, in either direction 
Neither the velocity at the surface nor the velocity at the 
bottom, nor, generally, the velocity at any determinate depthya is 
ei 
