surface is drifted to and fro, it undergoes no more ultimate change of
position than it would if the forces which acted upon it were
simultaneous and in equilibrium.'[9]

Of course, so simple a case as that in which the ebb and flood forces
are equal and opposite, is rarely presented; for at most of the stations
on the Bar the direction of the flow varies from hour to hour, going
quite round the circle in a half-tidal day: the velocities and
directions also vary with the depth. These circumstances complicate the
computation a little, but the problem is still simple and direct.
Everything depends upon the faithfulness of the observations.

The physical diagrams which have been plotted from the results of these
studies may be regarded as decided successes, for they show in most
cases that the shoals lie in the foci or in the equilibrium points of
the observed forces.

The current stations occupied cover a district embracing not only the
immediate vicinity of the shoals, but extending many miles from them in
different directions; for it was deemed necessary that each elementary
force should be separately studied before it reached its working point.
It has been ascertained that among the causes of the different shoal
formations there exists a mutual relation and dependence, so that they
may be regarded as a single physical system. _It will be seen from this
consideration, that any artificial disturbance of the conditions, at a
single point, may interrupt the operations of nature in other localities
more or less remote, or cause general changes in the hydrogaphy of the
harbor._

It is not simply the superficial drift of the tidal and other currents
that these observations comprehend; but, with the use of apparatus
suitably arranged, the movements at all depths have been determined,
with the exact amount of power exerted by streams coursing along the bed
of the sea. The necessity for this minuteness of examination has been
fully shown in some of the curious discoveries that have been made.

In several parts of our harbor, systems of counter-currents have been
detected, occupying strata of water at different depths, and these
present, in their motions, striking contrasts of directions, velocities,
and epochs. The most remarkable exhibition of these sub-currents was
observed in the neighborhood of the city, in the channel between
Governor's and Bedloe's Islands. In this locality, during the last
quarter of the ebb, float