gravity exerted directly on her by the moon. And, on the side of the earth facing the sun, she feels a centrifugal force produced by revolution around the centre of gravity of herself and the moon, and also a centripetal force produced by the gravitating influence of the sun. Hence there must be high tide also when sun and moon are in opposition.
It is a known fact that the solar are less than the lunar tides. How must we account for this fact? The sun is a body so large that the mass of the moon is not much more than a grain of sand in comparison with it. But it must also be remembered that gravity diminishes as the square of the distance increases; and as the moon is very near the earth, and the sun a great way off, the lunar influence is much more strongly felt in the phenomena of tides than the solar influence.
The amount of centrifugal force felt by a body moving in space around a centre depends, not only on the velocity with which it moves, but also upon the size of the curve in which it moves. If the circumference of the curve is very large, it differs not much from a straight line. If a body moves in space in the direction of a straight line, it feels no centrifugal force at all. If it is deflected from the direction of this straight line, only a very little, the circumference of the curve will be very long, and the centrifugal force will be small. But, if it is very much deflected, the curve becomes very small, and the body, turning around very "short corners," has a strong tendency to fly "off the track." In other words, in a short curve the centrifugal force is very great.
Now, let us make an examination of the orbital curve of the earth made in its motion around the sun. The length of the circumference of this curve is, in round numbers, about 570,000,000 miles. A straight line, 10,000 miles in length, tangent to this curve at one end, is only about .526 of a mile distant from the circumference at its other end. Therefore, the earth, moving in this orbital curve, feels rather a small amount of centrifugal force. But, in her motion around the centre of gravity between herself and the moon, she turns very "short corners," and hence under this influence she experiences a greater amount of centrifugal force than in her motion around the sun. For this reason, also, the lunar are greater than the solar tides.
If the earth had only one rotation in one revolution around the sun, there would be, as already stated, one solar tide by virtue of centrifugal force occurring at midnight, and another by virtue of centripetal force occurring at noon. That is, perpetual night and high tide would occur at one side, and perpetual day and high tide at precisely the opposite side of the earth. But now let us suppose the earth rotates on her axis once every twenty-four hours, and from west to east, as she actually does rotate: then there will be motion of the waters; but this motion will be only apparent motion, and from east to west.
