( 699 j 
and heat?). It follows directly from the application to this form of 
motion of the mechanical principle which has been exactly formulated 
by HeLMHoLTz, according to which the variation of the energy of 
an isolated system can only vanish °). 
According to the second principal law the variation of the entropy 
for an isolated system, which passes through a cyclical process, can 
only vanish or be positive %). The generality of this thesis is founded 
upon the additional hypothesis, that heat cannot of itself pass from 
a colder to a warmer body *). 
If we call « the energy of the system and 7 the entropy, then this 
thesis may be analytically represented by: 
(0 7). > 0 
where the subscript Jetter after a variation indicates the quantity of 
which the value is not to be varied. 
According to CLAustIus a cyclical process is defined as a series of 
changes through which the system passes, and through whieh it 
returns to its initial state ®). This series of changes can be reversible, 
in which case the sign of equality is to be applied, or quite or 
partly irreversible in which case the sign of inequality must be used. 
As perfectly reversible processes do not occur in nature, the sign of 
equality applies only to an ideal case to which the actual occurring 
cases more or less approach ®). 
But when for an isolated system which passes through a cyclical 
process, the variation of the entropy can only vanish or be positive, 
then such a system is in equilibrium when 
(Ön). <0 
for all possible variations of the state of the system which do not 
alter its energy 7). 
GiBBs has applied this eriterion, which is necessary and sufficient 
for equilibrium to a thermally, mechanically and chemically isolated 
system. In this he excluded the action of gravity, of capillarity and of 
electrical influences ®). The general condition of equilibrium leads to 
the following more special conditions of equilibrium’). 
') Crausrus, l.c. p. 24, 
2) HetmHoLtz, Ueber die Erhaltung der Kraft. Klass. d. exakten Wiss. N°. J. p. 14, 
3) Crausius, l.c. p. 93. 222. 
*) Crausius, lc. p. 8). 
*) Crausius, l.c, p. 35. 
6) Pranck, Thermodynamik. 1897, p. 79. 
7) Gipps, Transact. Conn. Acad. 1874—78, vol. III. p. 109, 
5) The electrical phenomena in physiological systems require a separate treatment, 
which rests, however, on the same basis. 
*) Gipps 1. ce, p. 115 e.sq. 
