340 THE POPULAR SCIENCE MONTHLY. 



Assuming the density of the earth to be 5^ 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 dur- 

 ing 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 

 42f minutes, and on its axis in the same time and in the same direc- 

 tion, 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 differ- 

 ence of the tangential force on the particles) ' would exactly counter- 

 balance 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 



1 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. 



