INTRODUCTION. XXxix 



resting on the height ; -^-V 2 is the kinetic energy corresponding to this potential 



energy (Brilcke). 



Potential energy may be transformed into mechanical energy under the most 

 varied conditions ; it may also be transferred from one body to another. 



The movement of a pendulum is a striking example of the former. When the pendulum is 

 at the highest point of its excursion, it must be regarded as absolutely at rest for an instant, 

 and as endowed with potential energy, thus corresponding with the raised stone in the previous 

 instance. During the swing of the pendulum this potential energy is changed into kinetic 

 energy, which is greatest when the pendulum is moving most rapidly towards the vertical. As 

 it rises again from the vertical position, it moves more slowly, and the kinetic energy is 

 changed into potential energy, which once more reaches its maximum when the pendulum 

 comes to rest at the utmost limit of its excursion. Were it not for the resistances continually 

 opposed to its movements, such as the resistance of the air and friction, the movement of the 

 pendulum, due to the alternating change of kinetic into potential energy and vice versa, would 

 continue uninterruptedly, as with a mathematical pendulum. Suppose the swinging ball of the 

 pendulum, when exactly in a vertical position, impinged upon a resting but movable sphere, 

 the potential energy of the ball of the pendulum would be transferred directly to the sphere, 

 provided that the elasticity of the ball of the pendulum and the sphere were complete ; the 

 pendulum would come to rest, while the sphere would move onward with an equal amount of 

 kinetic energy, provided there were no resistance to its movement. This is an example of the 

 transference of kinetic energy from one body to another. Lastly, suppose that a stretched 

 watch-spring on uncoiling causes another spring to become coiled ; and we have another example 

 of the transference of kinetic energy from one body to another. 



The following general statement is deducible from the foregoing examples : 

 If, in a system, the individual moving masses approach the final position of equi- 

 librium, then in this system the sum of the kinetic energies increases if, on the 

 other hand, the particles move away from the final position of equilibrium, then 

 the sum of the potential energies is increased at the expense of the kinetic energies, 

 i.e., the kinetic energies diminish (Briicke). 



The pendulum, which, after swinging from the highest point of its excursion, approaches the 

 vertical position, i.e., the position of equilibrium of a passive pendulum, has in this position 

 the largest amount of potential energy ; as it again ascends to the highest point of its excursion 

 on the other side, it again gradually receives the maximum of potential energy at the expense 

 of the gradually diminishing movement, and therefore of the kinetic energy. 



3. Heat. Its Relation to Potential and Kinetic Energy. If a lead weight be 

 thrown from a high tower to the earth, and if it strike an unyielding substance, the 

 movement of the mass of lead is not only arrested, but the kinetic energy (which 

 to the eye appears to be lost) is transformed into a lively vibratory movement of 

 the atoms.. When the lead meets the earth, heat is produced. The amount of 

 heat produced is proportional to the kinetic energy, which is transformed through 

 the concussion. At the moment when the lead weight reaches the earth, the atoms 

 are thrown into vibrations ; they impinge upon each other ; then rebound again 

 from each other in consequence of their elasticity, which opposes their direct juxta- 

 position; they fly asunder to the maximum extent permitted by the attractive force 

 of the ponderable atoms, and thus oscillate to and fro. All the atoms vibrate like 

 a pendulum, until their movement is communicated to the ethereal atoms sur- 

 rounding them on every side, i.e., until the heat of the heated mass is "radiated" 

 Heat is thus a vibratory movement of the atoms. 



