Although the sea as a whole keeps its level, yet in various parts it is constantly rising and sinking, sometimes at one place and sometimes at another; these risings and fallings are called tides, and are caused by the joint action of the sun and moon, that is, by their attraction, acting at different distances. First it must be observed (as is well known) attraction varies inversely as the square of the distance, that is, if the moon were twice as far off, her attraction of the earth would be one-fourth of what it now is, if three times as far off, one-ninth, and so on. The moon's average distance from the centre of the earth (A to C, in the diagram) is about 240,000 miles, or about 60 times the earth's radius (B C), which is a little under 4000 miles, consequently if the distance from the moon to the centre of the earth (A C) be expressed by 60, the distance to the nearest surface (A B) will be 59, and the farthest surface (A D) 61. The moon will attract the point B with a force of 1/59^2 or 1/3481, the point C with the force of 1/60^2 or 1/3600, and the point D with the force of 1/61^2 or 1/3721. Now as the force at C is greater than at D, the earth itself will be pulled away from the water at D, and leaving it a little behind, will produce a high tide there, this tide is known as the "inferior tide" (2). Again as the force at B is greater than at C, the water at B will be pulled away from the earth and produce a still higher tide, called the "superior tide" (1), or that which takes place when the moon is due south. This heaping-up of the waters by the moon, to the height of 4-1/2 feet (on an average) causes corresponding depressions to the same depth in those parts of the earth which are situated between the raised parts, making a difference between high and low-water of nine feet due to the moon; precisely the same effects are produced by the sun, but though his attractive power is so much greater than the moon's, his distance is also so much greater, that the heap of water he can raise is somewhat less than 2 feet, and makes therefore less than 4 feet difference between high and low-water, due to the sun. When the sun and moon are both on the same side, or on opposite sides of the earth (as at new or full moon), then the attraction of both act together and produce "spring tides," with a difference of 13 feet; at first and last quarter the sun and moon oppose each other, acting in cross directions, and the difference is then only 5 feet. But these effects could only take place in the wide open space of an ocean, and when other forces do not interfere, such as obstruction to the tide-waves by land, &c. [Illustration: DIAGRAM OF THE TIDES.]