readily driven in opposite directions by these opposite forces. If the earth were entirely solid, then there could be no such bulging out of any of its matter, and therefore no tides.
A few words here in regard to the law of gravitation are in place. Every body of matter attracts every other body of matter, and with a force equal to the amount of matter each body contains; and this force diminishes as the square of the distance increases. Two bodies of equal mass approach each other equally; but, if one body contains four times as much matter as another, the smaller approaches the larger with a velocity four times as great as the larger does the smaller. Suppose two such bodies, being separated at a distance of 100,000 miles, attract each other with a certain known force: if this distance be increased to 200,000 miles, the force of attraction between these two bodies will be only one-fourth as great. In like manner, the earth, at the point farthest from the sun, feels a smaller degree of attraction than the matter at the centre. And, as the centrifugal force is also greater at this point than at the centre, there is here an excess of centrifugal over centripetal force, and sufficient, as can be ascertained by exact mathematical calculation, to produce a solar tide. And at that part of the earth's surface which is nearest the sun, or facing it, there is, according to the same law of gravity, an excess of centripetal over centrifugal force. Hence we have also a solar tide at this part of the surface of the earth.
I give one more illustration. Suppose the earth, at E (Fig. 1), is moving in a straight line toward E and with a velocity of 68,000 miles an hour; and suppose when she reaches E' she comes under the
Fig. 1
attractive influence of the sun. She will then be deflected from her rectilineal course and move in a curvilineal orbit around the sun. That part of her surface turned away from the sun will be 8,000 miles farther from the attractive influence of the central orb than that part of her surface facing the sun. Hence this remote part will have a greater tendency to continue moving on in a straight line than any other part; and this tendency will show itself in the motion of its waters, by producing a tide. The waters will have a tendency to move in a line tangent to the orbit of the earth. The part of the
