24 HABIT AND INTELLIGENCE. [chap. i. 



other and only a hundredth of its mass, their momenta will be 

 Their equal ; but the smaller one will have a hundred times as much 



illnstrared ^^^^"^ ^^ motion as the larger. For instance : suppose a cannon 

 to be placed on a railway smooth enough to enable it to recoil 

 without any sensible friction ; and suppose a projectile of one 

 hundredth of the weight of the cannon to be fired from it, the 

 law of the conservation of momentum makes it necessary that 

 the position of the common centre of gravity of the cannon and 

 the projectile should be unchanged ; consequently the velocity 

 of each will be inversely as its mass, and the cannon will recoO. 

 with a velocity equal to a hundredth of that of the projectile. 

 Their momenta will consequently be equal ; but the energy 

 of motion of the projectile will be a hundred times that of 

 the cannon. 



Of course the quantity of heat, or of any other form of 

 energy that is produced when motion disappears, is due, not 

 to the momentum, but to the energy of motion ; not to the 

 velocity simply, but to the square of the velocity. 



