THE CONSTANCY OF MOTION 227 



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 me- 

 chanically, 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 weigh- 

 ing 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 in- 

 creased 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 attrac- 

 tion 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 proceed- 

 ing 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 mo- 

 tion 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, ca- 

 pable of doing tangible work when fitly permitted. Let us bring 



