PROFESSOR IN BERLIN 337 



Helmholtz now designates these two portions free and bound 

 energy. He shows that the processes which appear spontane- 

 ously in a state of rest, and at a constant and uniform tempera- 

 ture, and are maintained without help from external working 

 force, can only progress in such a direction that the free energy 

 diminishes. Among these are included the chemical processes 

 that begin and continue of themselves at constant temperature, 

 and, if the Law of Clausius held without limitation, it would be 

 the value of the free energy, not that of the total energy 

 indicated by the evolution of heat, which would determine the 

 direction in which chemical affinity can act. 



Helmholtz next undertook a general inquiry into any 

 compound system of masses having all the same temperature, 

 and all being subject to the same alterations of temperature, 

 and assumed that the state of the system was completely 

 determined by the temperature and by a number of inde- 

 pendent parameters. In a series of brilliant mathematical 

 deductions he arrived (by means of the two equations of 

 Clausius) at the result that it is only necessary for the repre- 

 sentation of thermodynamic equations to obtain the differential 

 quotients of the so-called ergal, which is absolutely determined 

 as a function of temperature. This ergal, for all alterations 

 occurring at constant temperature, coincides with the value 

 of the potential energy for the unrestrictedly convertible 

 quantity of work, and he calls it the free energy of the system, 

 while the difference between the total internal energy and 

 the ergal is termed the bound energy. The quotient of the 

 restricted energy by the temperature is the entropy of Clausius. 



In order, further, to distinguish what had till then been 

 known as vis viva, or kinetic energy, in theoretical mechanics 

 from the work-equivalents of heat (which indeed was for the 

 most part regarded as the vis viva of invisible molecular 

 motions), Helmholtz proposes to call the former the vis viva of 

 organized motion. As a general definition of organized motion 

 he gives that in which the velocity components of the masses 

 in motion may be taken as the continuously differentiate 

 functions of spatial co-ordinates. An unorganized motion, on 

 the contrary, is that in which the movement of each separate 

 particle exhibits no sort of similarity with that of its neighbours. 

 Heat motion may very probably be included in this mode, and 



