a centrifugal force that is in excess of the centripetal force felt at this same point; and the matter of her surface facing the sun, being nearest to it, feels a centripetal force that is in excess of the centrifugal force felt at this same point. But these two excesses are equal; hence there are equal solar tides at these points, while at the earth's centre there is an exact balancing of the two forces.
Suppose the matter of the earth were all condensed into the volume of a cubic inch, and that this small volume were placed at the earth's present centre; then suppose it received an impulse carrying it forward with a velocity equal to that which moves the centre of the earth, and that it were influenced by the sun, according to the law of gravity. This small volume, though equal in mass to the entire mass of the earth, would then move in the same curve in which the centre of the earth moves, and with the same velocity. But suppose this solid inch of matter were to be placed 4,000 miles farther from the sun, namely, at that point in space where the earth's surface is most remote from the sun. This solid inch, or whole mass of the earth, would then move in a longer curve than it would when at her present centre, as under the first supposition. But completing, nevertheless, in this longer curve, one revolution in the same time in which one revolution is completed in the shorter curve, at the earth's centre, the centrifugal force would be much increased; and, the centripetal force being also diminished in the same ratio, this cubic inch of matter would either abandon the sun's companionship entirely or make a new orbit of motion. In like manner are the waters of the earth operated on by centrifugal force at this point of the earth's surface. They have a tendency to fly off in a line tangent to the earth's orbit.
Now, suppose again that this condensed matter of the earth were placed at that point in space where the earth's surface is nearest the sun, namely, 4,000 miles nearer the sun than the centre of the earth is: then the whole mass of the earth's matter would move in a shorter curve than when placed at the centre, but, completing one revolution in no shorter period, the centrifugal force would be diminished; and, being also nearer to the sun, the centripetal force would be much increased by the central power of attraction. Therefore, this body of matter would, under this supposition, also leave its orbit, but it would be drawn toward the sun, and probably plunge into it. In the one case, the centrifugal being greater than the centripetal force, the body would fly from its centre of controlling power; in the other case, the centripetal being equally superior to the centrifugal force, the body would also be drawn out of its orbit, but dragged to the centre of controlling power. These suppositions are made to show, by way of illustration, the excessive force of each kind over its opposite, at opposite sides of the earth. And these equally excessive forces, acting in such opposite directions, cause the opposite solar tides. The particles of water, moving easily among one another, are
