138 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



The number a is calculated from the velocity of sound in air, 

 the series b from the latent heat of the vapours of aether, alcohol, 

 water, and oil of turpentine, c from the expansive force of the 

 vapour of water at different temperatures. Clapeyron's formula 

 for gas is, according to this, identical with Holtzmann's ; its 

 applicabihty to solid and liquid bodies remains as yet doubtful. 



V. The Force-equivalent of Electric Processes, 



Statical Electricity, — Machine electricity can act in two ways 

 as the cause of the generation of force ; in the first place, the 

 electricity itself moves with the body that bears it, in obedience 

 to its attractive or repulsive forces ; secondly, by its motion in 

 the body that bears it, heat is generated. The first mechanical 

 actions have, as is known, been deduced from hypothesis of two 

 fluids which attract or repel with a force inversely proportional to 

 the square of the distance ; so far as experiment has been com- 

 pared with theory, both have been found to agree. According to 

 our primitive deduction, the conservation of force must take place 

 with such forces. We will therefore enter only so far into the 

 more special laws of the mechanical actions of electricity as is 

 necessary for deducing the law of the electrical development of 

 heat. 



Let e^ and e^^ be two electric elements referred to a unit which 

 at the distance 1 repels an equal quantity of similar electricity with 

 the force 1. When the opposite electricities are distinguished 

 by opposite signs, and the distance between e^ and e^^ is called r, 

 the intensity of the central force is 



