CARNOT’S CYCLE IN THERMODYNAMICS.—MACGREGOR. 22m 
ART. V.—On CaRnNot’s CYCLE IN THERMODYNAMICS.—By PROF. 
J. G. MacGREGoR. 
(Received Jan. 16th, 1889.) 
The object of this paper, which is pedagogic rather than scien- 
tific, is to point out and remove a defect in the proofs usually 
given of the universality of the results obtained in Thermody- 
namics by the consideration of Carnot’s Cycle of Operations. 
From the Second Law of Thermodynamics it is proven that a 
Heat Engine has the greatest efficiency possible, provided, (1) it 
is reversible, and (2) when worked directly (2. @, so as to do 
external work), its “working substance” absorbs heat when at 
a high temperature, and emits heat when at a low temperature. 
The second of these two conditions is not generally specified in 
so many words by writers on Thermodynamics; but the argument 
by which the efficiency of the reversible heat engine is shewn to 
be the greatest possible always assumes that the heat engine 
referred to is one of the kind specified above. 
It is next pointed out that a substance subjected by the aid 
of Carnot’s Ideal Heat Engine to what is known as Carnot’s 
Cycle of Operations, in such a way that the cycle is reversible, 
constitutes a heat engine fulfilling both the above conditions. 
It follows that its efficiency is the greatest possible, and is inde- 
pendent of the nature of the working substance; and a result 
is thus reached which is of extreme importance, because of its 
perfect generality, 
The defect referred to above is in the proof that any substance 
whatever subjected to Carnot’s Cycle, in such a manner that it 
does external work, absorbs heat when at a high temperature 
and emits heat when at a low temperature. All wriiers* on 
Thermodynamics known to me, prove, not that this is true of 
any substance whatever, but only that it is true of one or two 
*T do not refer here to writers on air and steam engines, who rightly enough restrict themselves 
to a study of Carnot’s Cycle as applied to gases and saturated vapours. 
