the bay tended to be an expansion of water within the land not only
horizontally but vertically, and to form a basin or independent pond,
the direction of the two capes showing the course of the bar. Every
harbor on the sea-coast, also, has its bar at its entrance. In
proportion as the mouth of the cove was wider compared with its length,
the water over the bar was deeper compared with that in the basin.
Given, then, the length and breadth of the cove, and the character of
the surrounding shore, and you have almost elements enough to make out a
formula for all cases.

In order to see how nearly I could guess, with this experience, at the
deepest point in a pond, by observing the outlines of a surface and
the character of its shores alone, I made a plan of White Pond, which
contains about forty-one acres, and, like this, has no island in it, nor
any visible inlet or outlet; and as the line of greatest breadth fell
very near the line of least breadth, where two opposite capes approached
each other and two opposite bays receded, I ventured to mark a point a
short distance from the latter line, but still on the line of greatest
length, as the deepest. The deepest part was found to be within one
hundred feet of this, still farther in the direction to which I had
inclined, and was only one foot deeper, namely, sixty feet. Of course, a
stream running through, or an island in the pond, would make the problem
much more complicated.

If we knew all the laws of Nature, we should need only one fact, or
the description of one actual phenomenon, to infer all the particular
results at that point. Now we know only a few laws, and our result is
vitiated, not, of course, by any confusion or irregularity in Nature,
but by our ignorance of essential elements in the calculation. Our
notions of law and harmony are commonly confined to those instances
which we detect; but the harmony which results from a far greater number
of seemingly conflicting, but really concurring, laws, which we have not
detected, is still more wonderful. The particular laws are as our points
of view, as, to the traveller, a mountain outline varies with every
step, and it has an infinite number of profiles, though absolutely but
one form. Even when cleft or bored through it is not comprehended in its
entireness.

What I have observed of the pond is no less true in ethics. It is the
law of average. Such a rule of the two diameters not only guides us
toward the sun i