INTRODUCTION. XXV 



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 pen- 

 dulum, 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 diminish- 

 ing 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 pro- 

 duced 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 juxtaposition ; 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 surrounding them on every side, i.e., until the heat of 

 the heated mass is " radiated." Heat is thus a vibratory movement of the 

 atoms. 



As the amount of heat produced is proportional to the kinetic energy, 

 which is transformed through the concussion, we must find an adequate 

 measure for both forces. 



Heat-Unit. As a standard of measure of heat, we have the "heat- 

 unit" or calorie. The "heat-unit" or calorie is the amount of energy 

 required to raise the temperature of 1 gramme of water 1 centigrade. 

 The "heat-unit" corresponds to 425'5 gramme-metres, i.e., the same 

 energy required to heat 1 gramme of water 1C. would raise a weight of 

 425 '5 grammes to the height of 1 metre; or, a weight of 42 5 '5 grammes, 

 if allowed to fall from the height of 1 metre, would by its concussion, 

 produce as much heat as would raise the temperature of 1 gramme of 

 water 1C. The "mechanical equivalent'' of the heat-unit is, there- 

 fore, 425'5 gramme-metres. 



It is evident, that from the collision of moving masses, an immeasurable amount 

 of heat can be produced. Let us apply what has already been said to the earth. 

 Suppose the earth to be disturbed in its orbit, and suppose further that, owing to 



