a force equal to 1, when permitted to unite, have together a force less than 2; and this because work can be done by their attraction mechanically, or may appear as heat; and of course this must diminish their original stock of energy.
Precisely so with gravity. Suppose, for simplicity's sake, the radius of the earth to be 4,000 miles. Let us then imagine a stone of four tons lifted from the earth's surface to a distance of 4,001 miles; it would there weigh one ton—very nearly. Were such a mass to fall it would pass through 4,001 miles of space, and yield corresponding work.
Now let us further imagine a world, concentric with our present one, to be made up by the union of the earth with seven other such planets, and let us leave out of the question any possible condensation in the matter of this new world. Then supposing the stone to have resumed its former position in space, if gravity were allowed to act again, it could only do so through one mile, instead of 4,001 miles as before.
And mark how the geometrical necessities of enlargement lessen the working power of a mass attracting by gravity; for a stone weighing four tons on our present globe would only weigh twice as much on a sphere containing eight times the matter.
In the latter case, the surface would be twice as distant from the centre as in the former; for the attraction diminishes as the square of the distance of surface from the centre. Therefore the 8 times increased bulk has to be divided by 4, the square of the doubled radius.
Thus the weight of a definite mass on any celestial body varies as the density of the body and as the radius of it.
One of our pound-weights taken to the sun would there weigh 27 pounds, the sun's radius being about 110 times that of the earth, but its density only about one-fourth as great; while its bulk exceeds that of our planet by as much as 1,252,000 times.
If we now attentively observe the energy of a magnet in its usual genesis, we may learn somewhat, not only of gravity, but of attraction in general. The most convenient way to make magnets is by the use of an electric coil. A piece of properly-tempered steel is inserted in a helix of copper wire, through which a current circulates proceeding from the mechanical motion of a steam-engine, converted into electricity by suitable apparatus.
Other methods of magnetization there are, but none so directly instructive as this; here we have the visible, palpable motion of heavy wheels disappearing, and the chief result is the attractive force developed in the steel. The conviction dawns upon us that the motion of the wheels has been taken up by the molecules of the bar, that the steel has now internal movements which before it had not; and that these movements of its particles exist in full actuality, capable of doing tangible work when fitly permitted. Let us bring