TIDES LUNAR AND SOLAR The origin of the grand regular movement of the waters of the ocean, called the tide, may perhaps be more clearly explained by supposing the earth to be entirely covered with uni formly-deep water, and then observing the effects of the attrac tion of the moon and sun on this aqueous envelope. The student must, however, first of all, have a clear conception of that species of attraction called gravitation, or gravity, which is universal— every particle in nature attracting every other particle. The fundamental laws by which the attraction of gravitation is governed, relate to (1) mass, and (2) distance. First, the force of attraction between two bodies is in a direct ratio to their mass. That is, the larger the mass of a body, the greater its attractive power. Secondly, the force of attraction between two bodies is in an inverse ratio to the square of the distance; or, in other words, the attractive power of bodies decreases proportionately to the distance. Thus, suppose three bodies of equal mass— A, B, and C, attract a fourth body, D. If A, B, and C, are at equal distances from D, their attractive power will be the same, since they are of equal mass ; but if A be 250,000, B, 500,000, and C, 1,000,000 miles from D, their attractive force will be unequal, although their mass be still the same. Attraction diminishes as the square of the distance, therefore the attractive force of A will be four times as great as that of B, which is at twice the distance. The force of B will likewise be four times, and A's sixteen times, that of C. As, therefore, the attractive force of bodies is in a direct ratio to their mass, and decreases proportionately to the distance, a large-body may exert a stronger attractive force than a much nearer but smaller body ; and, vice versa, a smaller, but much nearer, body may attract another more strongly than a much larger, but more distant, body. Thus, supposing the mass of B to be four times that of A, both A and B would attract D equally, the greater distance of B being exactly balanced by its larger mass. Again, suppose C at four times the distance of A be only four times the size, then its attractive force on D would be only a fourth of that of A. Now the sun is 400 times further from the earth than the moon is, but his mass is nearly 28,400,000 times greater. If the sun's mass were equal to that of the moon, the earth would be attracted by the sim and moon in the proportion of 1 to 160,000: that is, the attraction of the moon would be 160,000 times greater than that of the sun, supposing their mass to be equal. But as the sun is 28,400,000 the size of the moon, its mass is so vastly greater, that the difference in distance is more than balanced. The sun there
fore attracts the earth as a toltole much more strongly than the moon does. We are now in a position to understand clearly the effect of the solar and lunar attraction on the earth. Let us consider that of the moon first, still retaining the supposition that the earth is entirely covered with uni formly-deep water.
As the earth revolves on its axis once every twenty-four hours, every part of its surface is successively brought under the direct action of the moon once a day. But the tide ebbs and flows twice a day, whereas if the tide were due to the simple attraction of the moon on the side of the earth nearest to it, there would only be one tide a day. This apparent ambiguity is easily explained. In the above diagram, the shaded circle represents the solid earth covered by uniformly-deep water, a, b, c, d, and the moon. But the attraction of the moon destroys the uniformity of the aqueous covering of the earth, for the latter has a diameter of nearly 8,000 miles, and the moon is only 240,000 miles distant—it is evident that the difference in the moon's attraction on the opposite sides of the earth will be very considerable. Both the solid and liquid portions of the earth are equally attracted in proportion to their distance, but the limited cohesion of the water allows it to respond to that attraction differently to the solid part, which can only move as a whole. The waters, therefore, on the side towards the moon, are drawn off from b and e towards d, and finally culminate at the point D. This bulging out at D is, then, due to the difference in the force of the moon's attraction on the water b, d, e, and on the solid crust B, D, E,—the water alone being free to move, is drawn towards the point of maximum attraction. Similarly, the moon's attraction on the opposite solid crust B, A, E, will be greater than on the water b, a, e; and as the solid part can only move as a whole, A, B, D, E, approaches .11 f, leaving the water behind, as it were, at A; so that here it bulges out exactly as at D. And as the waters culminate at A and D, they are drawn off from b and e, and finally sink to B and E. Supposing, then, that the earth were uniformly covered with water, and subject only to the moon's attraction, two tides would be formed—one on the side nearest the moon, and one on the opposite side—the culminating point in each being in the direct line of the moon's action. And as the earth revolved on its axis, the tidal waves thus formed would make the complete circuit of the globe once a day.