Assuming the density of the earth to be 52 times that of ice, it follows that, if a globe of ice—say ten miles in diameter—be isolated in space, a small dense body, as a bullet, near its surface, should fall toward it—by the action of its gravity alone—through 160 inches during the first minute of its descent. Now, if this icy globe be made to revolve around any large planet in the short period of 5 hours and 424 minutes, and on its axis in the same time and in the same direction, then the tidal energy (which is, in this case, the difference between the force of the planet's attraction for the particles at the centre of the icy satellite and for those at the two opposite points of its surface which are nearest to and farthest from the planet, added to the difference of the tangential force on the particles) would exactly counterbalance the icy satellite's interior gravity along this diameter; i. e., if the tidal energy could be made to act alone on the aforesaid bullet, at either end of this diameter, it would force it outward through 160 inches during the first minute of such action; hence, if a particle at either end of this diameter should be acted upon both by the gravity and the tidal energy at the same time, it would have no tendency to move in either direction; but if it were raised a few inches above the surface, then the tidal energy would prevail over the gravity and take it away.
To get a clear conception of the peculiar condition under which this icy globe is now placed, let us call this last-named diameter its axis of tension, and the plane passing through its centre and perpendicular to it the plane of compression.
Now, along this axis there is no force to prevent the elongation of the icy globe in that direction, except only the force of cohesion in the ice itself, as its gravity in that direction is exactly counterbalanced by the tidal energy.
Around the plane of compression, however, the case is different; here the interior gravity is unopposed by the tidal energy, and every atom is pressing inward on the central mass; and this pressure tends to force the tensible regions outward, and thus to make the tensile axis longer.
When this elongation begins, the disruptive energy rapidly increases in virtue of the increased diameter in that direction, and the diminution
- The above is the formula usually given for computing the tidal energy under the assumed conditions; but I incline to believe that the real disruptive power exerted on the satellite is just double that, for the following reasons:
One (1) pound of ice placed on the surface of this icy globe should press it with the force of 1.6 grain, of our standard.
Now, the tidal energy, as above calculated, causes the planet to pull the nearest pound with 1.6 grain greater force than it does the central pound, while, at the same time, it pulls the central pound with practically 1.6 grain greater force than it does the farthest pound; consequently the tensile pull between these two surface-pounds, which would be required to resist the tidal energy, must be equal to 2 x 1.6 grain, while they are drawn toward each other by the gravity of the satellite with the force of only 1.6 grain.