1903.] - HAUPI—DEEPER NAVIGABLE CHANNELS. 207 
is local, but when the resistance is maintained the reaction con- 
tinues to be developed and the energy to be expended until the 
resistance ceases. 
The great advantages resulting from a continous reaction pro- 
duced by a concave directrix appears to have been largely ignored | 
in the work of river and harbor improvement, and yet the location 
of the best channels under the concave banks of rivers attests its 
value to commerce. It is true that numerous curved dikes and re- 
vetments have been placed in the concave bends of rivers, but the 
object has been to protect them /vom erosion and not to encourage 
it. Their value as tools to cut away an ocean bar does not appear 
to be fully appreciated, since where single curved jetties have been 
built the convex face has generally been turned to the current, to 
encourage, as has been said, the tendency which water has to 
follow a convex curve. (?) 
The concave directrix has also the great advantage of maintain- 
ing the head due to centrifugal force and thus changing the direc- 
tion of the resultant downwardly, producing the lateral scour and 
resulting convex bank or counterscarp created by the stream acting 
as an hydraulic auger, and of automatically adjusting this counter- 
part to the variable requirements of its regimen. 
These general principles will be more fully elucidated by illustra- 
tions selected from surveys and models, showing the holes bored by 
reaction and the shifting of channels by artificial works, which are 
instructive.as to the intimate relation between cause and effect. 
A study of the natural effects found to exist under certain condi- 
tions enables the engineer to predict with some assurance the results 
which may follow a utilization of the available forces at any site. 
One of the most instructive examples of the vertical eddy is to be 
seen in the Narrows at New York, to which reference has already 
been made. Here the bottom currents are with the flood tide for 
about eleven hours out of the twelve, and this resultant flood ex- 
tends as far up as the Battery. The ebb resultants are greatest at 
the surface and diminish rapidly with the depth, reaching their point 
of reversion at or near forty feet in the Narrows. On the bar the 
ebb currents show a feeble resultant at a depth of less than twenty- 
four feet in but one of the channels. 
The remarkable ‘‘slue’’ which has maintained its position athwart 
the path of the currents since the earliest surveys has excited some 
attention as to its phenomenal position and depth of fifty-two feet. 
