n22 Prof. W. McF. Orr on Clausius’ 
His argument, which is specially designed to meet the 
objections of Bertrand mentioned above and alluded to by 
him, is much the same as Parker’s but presented at tedious 
length. 
He afterwards supposes each term of the integral divided 
into two, one corresponding to heat received from external 
bodies, the other to heat received from other portions of the 
system, and endeavours to establish a similar theorem for 
the integral of the set of terms relating to the former alone. 
If 8 is the temperature of a body which receives heat, I do 
not see how the source of the heat is to be identified, unless 
processes of radiation are excluded ; such a distinction thus 
seems untenable. 
Kirchhoff’s proof * also is somewhat similar to that given 
by Parker, except that Clausius’ version of the Second Law 
is adopted instead of Lord Kelvin’s. It is proved only, 
however, that the integral cannot be positive. And it is stated 
that the idea of entropy applies to reversible (‘‘ umkehrbare ”) 
processes only. 
Voigt adopts + the proof of Kirchhoff. 
In the case of the above writers and continental authors 
generally, it appears doubtful whether they intend to assert 
that the integral is negative or merely that it cannot be 
positive. 
Buckingham { states that all so-called proofs which have 
been given of the theorem appear to contain an unproven 
assumption, and regards the theorem as 4 new experimental 
principle forming a pendant to Carnot’s principle. 
No proof that Entropy is increased by an Irreversible Process 
can be deduced from the Laws of Thermodynamics as 
usually stated. 
20. It is here maintained then, in the first place, that any 
statement of the kind that in an irreversible process the 
entropy continually increases is meaningless ; and in the second, 
that in none of the discussions alluded to is the theorem that 
when a system passes in an irreversible way from one equi- 
librium state to another, without interchanging heat with 
external bodies, the entropy in the final state is greater than 
in the initial logically deduced from clearly stated premisses. 
From the latter contention, Planck’s proot must of course be 
excepted : it is valid only, however, because of the unusual 
* Theorie der Wirme, S. 58, 
+ Thermodynamk, Band i. Art. 124. 
{ ‘Thermodynamics,’ p. 153. 
