Page:Popular Science Monthly Volume 11.djvu/290

276 earth's surface nearest the sun, being acted upon more powerfully by the gravitating influence of this central force than the remote part, will show a less tendency to move on in a line tangent to the earth's orbit. Hence there will be another tide produced by gravity directly.

I have thus far spoken only of the solar tides. It will be necessary also to say something of lunar tides, or what influence the moon has on the phenomena of the tides.

It is a well-known fact that there is a point between the earth and her moon called their centre of gravity. The distance between the centres of these two bodies is about 240,000 miles. A rough calculation brings the centre of gravity of these bodies about 2,687 miles from the centre of the earth, and 237,313 miles from the centre of the moon. This point describes the curve of an ellipse around the sun; and the earth and moon revolve around this point, while they both sweep through space in their majestic journey around the sun. It is therefore evident that the earth, in her ceaseless motions, is influenced by three different centrifugal forces. The one is produced by rotation on her axis; the other by her revolution around the sun; and the third by her revolution around the centre of gravity between herself and the moon.

Let us suppose that the earth and moon have no other motion in space than that of revolving around their common centre of gravity, and that the same side of the earth is always facing the moon. The earth will then feel a centrifugal force on her side farthest from the moon, and equal to the centripetal force felt on her side facing the moon. These two equal forces, acting in opposite directions, will cause tide-waves on opposite sides of the earth; and they will be produced in the same manner as the opposite ones, spoken of already, are produced by centrifugal and centripetal forces felt by the earth in her orbital motion around the sun.

Let us now place the earth and moon in their proper position with respect to the sun; and let us suppose the moon to be in conjunction with the sun, as at A Fig, 2. It is then new moon, and the moon's centre is 237,313 miles within and the earth's centre 2,687 miles outside the elliptic orb described by their centre of gravity. At this point of her path the earth feels, therefore, the greatest amount of centrifugal force on the side of her surface farthest from the sun. This large amount of centrifugal force is produced by axial rotation, by revolution around the sun, and by revolution around the centre of gravity already named. The direction of these three forces is in the same line. The motion of this part of her surface, which is in this line of direction, is therefore the most rapid; consequently, the centrifugal force felt here is also the greatest. Therefore, we have one of the highest tides when the moon is in conjunction with the sun; and, since centripetal is always equal to centrifugal force, the side of the