520 Prof. W. McF. Orr on Clausius’ 
depend solely on the irreversible transference of heat, and 
the theorem would then have no reference to the generation 
of heat by “friction.” How is heat thus generated by 
“‘ friction ” to be distinguished from heat received from out- 
side? These difficulties would apparently be of less 
importance in another mode of stating the theorem in which 
6H and @ refer to an external system, though in that case 
there are other points of difficulty to be considered. 
I proceed to comment on some proofs of the theorem in 
cases in which it (the theorem) may be admitted to be 
intelligible. 
Clausius’ Proof. 
17. Clausius * himself stated the proposition in the forms :— 
The algebraical sum of the Transformations occurring in a 
cyclical process can only be positive or as a limiting case 
zero ;” and ‘‘Uncompensated Transformations can only be 
positive.” 
He did not explicitly state that the limiting case referred 
to in the first form can only occur if the process is reversible. 
He has, however, usually been interpreted in this sense, and 
apparently without objecting to it. As regards proof, he 
merely pointed out that the argument by which he had shown 
that in a reversible cycle the algebraical sum of the Trans- 
formations is zero, holds so far as to prove that in an 
irreversible cycle the sum cannot be negative, but fails to 
show that it cannot be positive, and that on the contrary 
there may very well be a balance left over of positive trans- 
formations. Not only the argument, but also the statement 
seems too obscure to have any claim to general validity. One 
would prefer nowadays to modify somewhat in the direction 
of greater precision the language of Clausius ; in endeavouring 
to make clear, however, one runs the risk of misinterpreting. 
Taking, however, the most favourable view, one cannot regard 
Clausius as having proved more than that in an irreversible 
cycle (\F cannot be positive and may be negative. 
Parker's proof. 
18. Of the discussions with which I am acquainted, the 
one which appears least unsatisfactory is that given by 
Parker f. Here all the heat absorbed (algebraically) by each 
small portion of the system is supposed to be imparted by a 
* Mechanische Warmetheorie, i. chap. x., or Browne’s translation. | 
f¥ ‘Elementary Thermodynamics,’ 1891, Art. 61. 
