As I sounded through the ice I could determine the shape of the bottom with greater accuracy than is possible in surveying harbors which do not freeze over, and I was surprised at its general regularity. In the deepest part there are several acres more level than almost any field which is exposed to the sun, wind, and plow. In one instance, on a line arbitrarily chosen, the depth did not vary more than one foot in thirty rods; and generally, near the middle, I could calculate the variation for each one hundred feet in any direction beforehand within three or four inches. Some are accustomed to speak of deep and dangerous holes even in quiet sandy ponds like this, but the effect of water under these circumstances is to level all inequalities. The regularity of the bottom and its conformity to the shores and the range of the neighboring hills were so perfect that a distant promontory betrayed itself in the soundings quite across the pond, and its direction could be determined by observing the opposite shore. Cape becomes bar, and plain shoal, and valley and gorge deep water and channel.
When I had mapped the pond by the scale of ten rods to an inch, and put down the soundings, more than a hundred in all, I observed this remarkable coincidence. Having noticed that the number indicating the greatest depth was apparently in the centre of the map, I laid a rule on the map lengthwise, and then breadthwise, and found, to my surprise, that the line of greatest length intersected the line of greatest breadth exactly at the point of greatest depth, notwithstanding that the middle is so nearly level, the outline of the pond far from regular, and the extreme length and breadth were got by measuring into the coves; and I said to myself, Who knows but this hint would conduct to the deepest part of the ocean as well as of a pond or puddle? Is not this the rule also for the height of mountains, regarded as the opposite of valleys? We know that a hill is not highest at its narrowest part.
Of five coves, three, or all which had been sounded, were observed to have a bar quite across their mouths and deeper water within, so that 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 in the system and the heart in man, but draws lines through the length and breadth of the aggregate of a man's particular daily behaviors and waves of life into his coves and inlets, and where they intersect will be the height or depth of his character. Perhaps we need only to know how his shores trend and his adjacent country or circumstances, to infer his depth and concealed bottom. If he is surrounded by mountainous circumstances, an Achillean shore, whose peaks overshadow and are reflected in his bosom, they suggest a corresponding depth in him. But a low and smooth shore proves him shallow on that side. In our bodies, a bold projecting brow falls off to and indicates a corresponding depth of thought. Also there is a bar across the entrance of our every cove, or particular inclination; each is our harbor for a season, in which we are detained and partially land-locked. These inclinations are not whimsical usually, but their form, size, and direction are determined by the promontories of the shore, the ancient axes of elevation. When this bar is gradually increased by storms, tides, or currents, or there is a subsidence of the waters, so that it reaches to the surface, that which was at first but an inclination in the shore in which a thought was harbored becomes an individual lake, cut off from the ocean, wherein the thought secures its own conditions — changes, perhaps, from salt to fresh, becomes a sweet sea, dead sea, or a marsh. At the advent of each individual into this life, may we not suppose that such a bar has risen to the surface somewhere? It is true, we are such poor navigators that our thoughts, for the most part, stand off and on upon a harborless coast, are conversant only with the bights of the bays of poesy, or steer for the public ports of entry, and go into the dry docks of science, where they merely refit for this world, and no natural currents concur to individualize them.
As for the inlet or outlet of Walden, I have not discovered any but rain and snow and evaporation, though perhaps, with a thermometer and a line, such places may be found, for where the water flows into the pond it will probably be coldest in summer and warmest in winter. When the ice-men were at work here in '46-7, the cakes sent to the shore were one day rejected by those who were stacking them up there, not being thick enough to lie side by side with the rest; and the cutters thus discovered that the ice over a small space was two or three inches thinner than elsewhere, which made them think that there was an inlet there. They also showed me in another place what they thought was a "leach-hole," through which the pond leaked out under a hill into a neighboring meadow, pushing me out on a cake of ice to see it. It was a small cavity under ten feet of water; but I think that I can warrant the pond not to need soldering till they find a worse leak than that. One has suggested, that if such a "leach-hole" should be found, its connection with the meadow, if any existed, might be proved by conveying some, colored powder or sawdust to the mouth of the hole, and then putting a strainer over the spring in the meadow, which would catch some of the particles carried through by the current.
While I was surveying, the ice, which was sixteen inches thick, undulated under a slight wind like water. It is well known that a level cannot be used on ice. At one rod from the shore its greatest fluctuation, when observed by means of a level on land directed toward a graduated staff on the ice, was three quarters of an inch, though the ice appeared firmly attached to the shore. It was probably greater in the middle. Who knows but if our instruments were delicate enough we might detect an undulation in the crust of the earth? When two legs of my level were on the shore and the third on the ice, and the sights were directed over the latter, a rise or fall of the ice of an almost infinitesimal amount made a difference of several feet on a tree across the pond. When I began to cut holes for sounding there were three or four inches of water on the ice under a deep snow which had sunk it thus far; but the water began immediately to run into these holes, and continued to run for two days in deep streams, which wore away the ice on every side, and contributed essentially, if not mainly, to dry the surface of the pond; for, as the water ran in, it raised and floated the ice. This was somewhat like cutting a hole in the bottom of a ship to let the water out. When such holes freeze, and a rain succeeds, and finally a new freezing forms a fresh smooth ice over all, it is beautifully mottled internally by dark figures, shaped somewhat like a spider's web, what you may call ice rosettes, produced by the channels worn by the water flowing from all sides to a centre. Sometimes, also, when the ice was covered with shallow puddles, I saw a double shadow of myself, one standing on the head of the other, one on the ice, the other on the trees or hillside.