436 A. C. Baines—The Deflection of Streams. 
the velocity and the angle @ varies at every point along a line 
drawn across the stream. Suppose the water to be divided 
into a number of small vertical columns, then the above rea- 
soning applies to each column and the forces acting on each 
will be similar in difection though differing in intensity, and 
there will be a transverse motion of the water, the surface and 
bottom layers moving in opposite directions, and necessarily a 
downward motion at the right bank, and an upward motion at 
the left. The resultant transverse force is greatest at the bot- 
tom and surface, and diminishes to nothing at the layer whose 
velocity is ¥,. 
The transverse motion must be extremely slow, and will be 
combined with that down the stream, so that the actual motion 
will be inclined at a very small angle to the direction of the 
channel. It is clear that a very slow motion of the bottom - 
shelving, and the right steeper, and to place the deepest part 
of the stream near the right bank, thereby increasing the 
velocity, and consequently the erosion. The left shore being, 
more shelving, will be more favorable to the resting of sedi- 
ment during floods. The deposition at the left bank explains 
how it is that a stream can cut away a high terrace on one 
side, the low-lying shore on the other being added to instead 
of being removed. 
The expression for the resultant transverse force on a par- 
2n sin v,—v 
ticle at the bottom, , v being the velocity at 
the bottom, may be used to oe. a rough approximation to the. 
force urging the bottom layer towards the left bank. Suppose 
(v,—v) = two feet per second, the latitude 45°. The expres- 
sion becomes 
W X2x0-0000729x0-707x2_ SW 
32° ~ 156230 
nearly, 
a 
underflow in the opposite direction. It is clear, therefore, that 
the deflecting and centrifugal forces must be added or subtracted, 
as the convex side is on the right or left side of the stream. 
Christchurch, New Zealand. 
