Theorem for Irreversible Cycles. 523 
definition of irreversibility, and, as has been pointed out 
above, the words in which this definition is expressed are not 
happily chosen. It is further contended, along with Parker 
and with Buckingham, that if an irreversible process be 
defined merely as one such that the successive states cannot 
occur in the reverse order in point of time, with all the 
motions, heat exchanges, chemical, electrical, and other 
changes, exactly reversed, and the mechanical forces un- 
altered *, it is impossible to deduce the theorem from the Laws 
of Thermodynamics in the form in which they are usually 
stated. It may be established for a few simple cases which 
are as much ideal as the reversible cycles usually discussed. 
Yet no one doubts its truth. Our belief in it seems based 
either on an induction from these simple cases in which it 
may be proved deductively, or on a deduction from premisses 
which include some property of irreversible (or natural) 
processes not stated explicitly but merely implied. 
Suggested modification of the Statement of the 
Second Law. 
21. Such a property may be stated explicitly in various 
forms. One form would constitute a slight amendment of 
Lord Kelvin’s version of the Second Law. Besides stating, 
as that version does, that if a system in a cycle interchange 
heat with external bodies it is impossible that in every inter- 
change the system should receive heat, we might add a 
further statement to the effect that if any process in the 
cycle is one which is actually possible with natural bodies, 
the system must at some stage give out heat. It is not of 
course suggested that such an addition embodies any new 
principle ; it is, in fact, merely another mode of stating that 
all actually possible processes are “irreversible ”’ in Planck’s 
sense (“irreversibel”?), which Planck himself appears to 
regard as axiomatict. For the statement that if an isolated 
system passes from one state to another by a process which is 
actually possible, it cannot, even by the aid of ideal reversible 
(“umkehrbare”’) processes, be passed back to its original 
state without interchanging heat with some external body, is 
equivalent to the statement that if a system undergoes a 
* IT do not think that there is anything in the idea of reversibility 
per se which requires us to restrict its application to a mere succession 
of equilibrium states. The motions of rigid frictionless bodies, or the 
vibrations of perfectly elastic bodies, as treated in dynamics, are instances 
to the contrary. | 
7 “.... Irreversible processes, which in fact are the only real processes 
in Nature....” Electrician, Feb. 13, 1903. 
