125. Pressure in Liquids Equal in all Directions.—We are now prepared to go a step farther. The pressure occasioned by gravitation in fluids operates equally in all directions when the fluid is at rest. That is, any particle of a liquid is pressed equally in all directions. If it were not so it would not remain at rest, but would be moved in the direction in which the superior pressure operates. Suppose that a, Fig. 79, is a stratum of particles in a vessel containing water at rest. The upward pressure on it being equal to the downward pressure, the stratum neither rises nor falls. If a body of liquid be disturbed by wind or any other cause, those particles which are raised above the common level in waves are pressed downward more than upward or laterally in obedience to the action of gravitation. They therefore move downward, pushing laterally and upward the neighboring particles, till the liquid regains its level surface and its state of rest. So, also, if any particles become heated they are lighter than their neighboring particles, and the latter being more strongly attracted than the former, push them upward in order to take their places. When all the liquid comes to have the same temperature it is at rest, each particle having an equal pressure upon it in all directions.
Fig. 80.
126. Illustrations.—If a bladder filled with water be compressed by the hand, the water is pressed no more immediately under the hand than in any other part of the bladder, and wherever an opening be made the water will rush out with equal readiness. A hose-pipe as readily bursts upward as in any other direction. A large cork, if sunk in very deep water, will be uniformly reduced in its dimensions, showing that it has been pressed equally on all sides. In the experiments with the closed bottles (§ 121), the result is the same if the bottle be so sunk as to have its mouth downward. If two tubes, shaped as in Fig. 80, be thrust down into water, the water will rise with equal facility in both, although in the straight one the pressure which carries up the water is wholly upward, while in the bent one it is at the first downward.
Fig. 81.
127. Upward Pressure as the Depth.—It has been shown that the downward and the lateral pressures are as the depth. The same is true of the upward pressure, for it is produced by the same cause—the attraction of the earth. Let us look at this. Why is any particle of a fluid pressed upward at all? It is from the struggle on the part of the neighboring particles to get below it. And why this struggle? It is from the attraction of gravitation, and so the greater this attraction the greater is the upward as well as the downward pressure. The upward pressure therefore differs at different depths as the downward pressure does. Thus, in Fig. 81, the upward pressure against the layer or stratum of particles, b, is greater than that against a, for the same reason that the downward pressure on b is greater than that on a. But the two pressures at b are equal, and so are they at a, and therefore each stratum remains at rest.
Fig. 82