JO SI All WILL ABB GIBBS 553 



temperature, or in Lord Kelvin's phrase, a general dissipation of 

 energy in all irreversible phenomena. For each potential, with appro- 

 priate choice of coordinates, a solid model or relief map can be con- 

 structed, upon which the different minima of the potentials appear as 

 depressions in the landscape. When the lowest depression or minimum 

 has been reached, complete and permanent equilibrium is attained, 

 and we have what Gibbs calls a " phase of dissipated energy," at which, 

 as in a bar of metal or a block of granite, no further spontaneous 

 changes of physical state are possible so long as the system remains 

 isolated from external forces. In connection with his discussion of 

 equilibrium we may note Gibbs's forethought in extending his equa- 

 tions to n dimensions, since for more than three components a three- 

 dimensional model no longer suffices ; his early introduction of the time 

 element into the discussion of chemical reactions*^ and his pages on 

 " passive resistance to change,"^* which should be read by every chem- 

 ist, since they are of the essence of his subject, especially in regard to 

 carbon compounds or colloidal substances. In applying dynamic prin- 

 ciples to chemical phenomena Gibbs, and after him Helmholtz, thought 

 decrease of free energy at uniform temperature to be the most impor- 

 tant condition for equilibrium, since it measures the actual work done 

 and is thus the " force function " of mechanics with reversed sign.^^ 

 The electromotive force of a reversible galvanic cell turns out to be 

 ident^'cal with the free energy of chemical decomposition in the cell,®* 

 and in the field of biology free energy is of equal importance, for rela- 

 tive uniformity of temperature is as common in living processes as in 

 the laboratory. Well did Boltzmann say that " the struggle for exist- 

 ence of living matter is a war for free energy," for when the free 

 energy of a living body becomes a minimum its death is at hand. 



The Phase Bule.^"^ — Any aspect of a chemical substance which is 

 homogeneous in regard to physical state and percentage composition 

 has been called by Gibbs a phase of the substance, the components of 

 a phase being its constituents of independently variable concentration. 

 The phase rule asserts that a homogeneous substance having n com- 

 ponents is capable of only n -\-l independent phases, while a hetero- 

 geneous system of r coexistent phases, each of which has n independ- 



•" Gibbs, loc. cit., 113. 



^*Ibid., 111-3. 



•» See Gibbs, Am. J. Sc, 1878, 3. s., XVI., 442. " The transition from the 

 systems considered in ordinary mechanics to thermodynamic systems is most 

 naturally made by this formula . . . the mechanical properties of a thermo- 

 dynamic system maintained at constant temperature being such as might be 

 imagined to belong to a purely mechanical system, and admitting of representa- 

 tion by a force function." 



•• Gibbs, Tr. Connect. Acad., III., 520. 



"^liid., 152-6. 



VOL. LXXIV. — 36. 



