MATTER, LIVING FORCE AND HEAT. 5 



in order to distinguish the moving force from that which is 

 stationary in its character, as the force of gravity. When, 

 therefore, in the subsequent parts of this lecture I employ the 

 term living force, you will understand that I simply mean 

 the force of bodies in motion. The living force of bodies 

 is regulated by their weight and by the velocity of their 

 motion. You will readily understand that if a body of 

 a certain weight possess a certain quantity of living force, 

 twice as much living force will be possessed by a body of 

 twice the weight, provided both bodies move with equal 

 velocity. But the law by which the velocity of a body 

 regulates its living force is not so obvious. At first sight 

 one would imagine that the living force would be simply 

 proportional to the velocity, so that if a body moved 

 twice as fast as another, it would have twice the impetus 

 or living force. Such, however, is not the case ; for 

 if three bodies of equal weight move with the respective 

 velocities of I, 2, and 3 miles per hour, their living 

 forces will be found to be proportional to those numbers 

 multiplied by themselves, viz., to 1 x 1, 2x2, 3x3, or 

 1, 4, and 9, the squares of 1, 2, and 3. This remark- 

 able law may be proved in several ways. A bullet fired 

 from a gun at a certain velocity will pierce a block of wood 

 to only one quarter of the depth it would if propelled at 

 twice the velocity. Again, if a cannon-ball were found to 

 fly at a certain velocity when propelled by a given charge 

 of gunpowder, and it were required to load the cannon so 

 as to propel the ball with twice that velocity, it would be 

 found necessary to employ four times the weight of powder 

 previously used. Thus, also, it will be found that a railway- 

 train going at 70 miles per hour possesses 100 times the 

 impetus, or living force, that it does when travelling at 

 7 miles per hour. 



