518 Prof. W. McF. Orr on Clausius’ 
The latter stresses depend on the amounts of the distortions ; 
viscous fluid stresses depend on the rate at which distortion 
is taking place. 
Planck’s Definition of Entropy of a Body other than a 
perfect gas not in a state of equilibrium. 
12. Planck defines the entropy @ of a body other than a 
"dU + pdV é 
eee according to 
the views put forward here even this definition is meaningless 
except for equilibrium states. 
perfect gas by the equation: @= 
Values of Entropy can be compared only in states of 
equilébrium. 
13. I submit then, following Bertrand, that no definition 
of entropy has yet been given (with the doubtful exception 
of Planck’s for a perfect gas) which is applicable to any states 
but those of relative equilibrium, and accordingly that any 
statement that entropy increases should be restricted to a 
comparison between its values in such states. 
A shorter proof of the principle of Increase of Entropy if 
the substance of Planck’s definition of “ Irreversibility ” 
be adopted. 
14. Again, the proof of the general theorem that when a 
system of bodies passes by means of an “irreversible” 
(‘‘irreversibel ”) process from one state, A, to another, B*, 
without exchanging heat with any external body, the entropy 
in the final state is greater than in the initial, could apparently 
be put more briefly, and without recourse to the perfect-gas 
system, as follows :—Let each small portion of the system be 
restored from the state B to the state A by an isothermal 
adiabatic process, in which every transference of heat which 
takes place is to or from the working substance of a perfectly 
reversible engine working between the temperature of the 
particle considered and an external body at a fixed tempera- 
ture, 0) (on Lord Kelvin’s absolute scale). The heat received 
by this external body is evidently the product of 6) and the 
excess of the value of the united entropies of the system in 
the state B over that in the state A. The system has now passed 
through a cycle starting from, and ending in, the state A. 
The heat received by the external body therefore cannot be 
* Tt is supposed that for each of these states it is admitted that entropy 
has a meaning. 
