18 



HABIT AND INTELLIGENCE. 



[chap. 



Conserva- 

 tioa of 

 areas, a 

 spiony- 

 mous term 

 with. 



conserva- 

 tion of 

 rotation. 



may be drawn either tlirougli, or outside of, the system 

 of bodies in question ; but for the piu'pose of forming a 

 clear mental representation of the subject, let us suppose 

 it drawn through the centre of gravity of the system 

 of bodies, and at right angles to the principal plane of 

 rotation. (For the solar system, this is nearly the same as 

 drawing it in the line of the sun's axis of rotation.) From 

 this axis, and at right angles to it, let a radius vector be 

 drawn to every indefinitely small part of the bodies, all 

 such parts being supposed of equal mass. Then the 

 algphraic sum of the prochocts of the radii vectores into the 

 tangential comjMnents of the velocities loill he a constant 

 quantiti/. Or, to state the law in a slightly different form : 

 the algebraic sum of the areas swept over hy the radii vectores 

 will he equal for equal times. 



In allusion to this latter mode of statement, the law of 

 the Conservation of Eotation is often called the law of the 

 Conservation of Areas. What is still called Kepler's 

 second law, namely, that the radius vector of every planet 

 sweeps over equal areas in equal times, is the best known 

 instance of the law of the conservation of rotation or of 

 areas. In consequence of the perturbations which the 

 mutual attractions of the planets produce in each other's 

 motions, Kepler's Second Law is not absolutely true of 

 any one planet ; but it would be so, if the solar system 

 consisted only of the sun and a single planet. 



Conserva- 

 tion of 

 energy. 



Trans- 

 formation 

 of energy. 



IV. The Conservation of Energy. — Energy, like 

 Matter, can he neither produced nor destroyed hy any process 

 vjhatever. Or, in other words : Whatever quantity of energy 

 has heen eocpended in doing work, reappears as energy. 



The conservation of energy, like the conservation of 

 matter, is contrary to appearance. But energy, like matter, 

 when it appears to be destroyed is really transformed. 

 For instance, when a railway train is stopped by the action 

 of the break, or when a cannon-ball sticks fast in a bank 

 of earth, the energy of motion which has disappeared is 

 transformed into heat. The heat that is produced by 

 mechanical action, such as friction or collision, is not a 



