hej 
APRIL 14, 1904 
NATURE 
563 
values of the volume of a pound of steam happens to 
be wrong. 
He says (p. 68), ‘‘ The whole nomenclature of thermo- 
dynamics demands re-modelling.’’ Of course we all 
know that there is much in scientific nomenclature 
which we should like to re-arrange, but his sweeping 
denunciations are mostly applied to things that are 
quite correct. For example, ‘‘ To measure the heat 
received at constant pressure or temperature by a 
‘specific heat at constant pressure ’ or ‘a specific heat 
at constant temperature ’ is absurd.’’ The book is full 
of this sort of statement, delivered with the air of Cato 
the Censor, accompanied by very clever un-Cato-like 
gibing such as might be expected in a cheap monthly 
magazine when the writers are poking fun at scientific 
persons. 
It is often quite impossible to find out the author’s 
line of thought. For example, on p. 50, where he 
says, ‘‘d¢ on the other hand is a complete differential 
in terms of the ordinates of the state diagram in which 
pv=R2, but it is not a complete differential with refer- 
ence to the external work or piston co-ordinates 
of the Watt diagram.’? No reader of this book 
can fail to notice that Mr. Swinburne has some 
novel idea as to the meaning of ‘ta complete differ- 
ential,’ and I have given much thought to the 
above cryptic statement hoping that it would 
throw light upon this interesting matter, but, 
alas! it still rests in the deepest kind of obscurity. 
Want of clearness does seem, somehow, to be inherent 
ain his study of this ‘‘ slippery ’’ subject, for in a foot- 
note (p. 35) he states that ‘‘ Rankine is not clear about 
his ‘thermodynamic function’’’ (now called entropy 
by orthodox persons). ‘‘ He certainly did not develop 
the idea of entropy and its relation to waste which 
forms the basis of this book. No doubt a man of his 
ability, if he had written on steam engines somewhat 
later ’’ (Rankine’s book on steam engines, published in 
1859. is not altogether unknown), ‘‘ would have been 
not only perfectly correct, but also clear and un- 
ambiguous in his statements and definitions.’’ It is 
evident that Rankine and Bahram, the great hunter of 
Omar Khayyam, have something in common, and that 
in this note Mr. Swinburne departs more than usual 
from the attitude promised by him on p. 4, that he 
was not writing ‘‘in any spirit of superiority.’’ One 
is inclined to use the language of Tennyson addressing 
Bulwer Lytton, ‘‘ What, 'you a Timon, .. .!”’ but it 
is better not to quote the words; they are omitted from 
the later editions of Tennyson. 
Probably the obscurity. is deepest in connection 
with the meaning of a pv diagram. He says 
(p. 49), ‘‘ There is considerable confusion as to 
the meaning of a pu diagram; that is to say, as 
to what p means in an irreversible change. As a pu 
or Watt diagram is ...’’ I beg to tell Mr. Swin- 
burne that a Watt diagram is not what anybody means 
(unless when speaking casually and hurriedly) by a 
py diagram; that in thermodynamics ‘we are dealing 
with ‘a quantity’ of stuff the v, p and t of which are 
supposed’to be ‘known at. each instant, and that if we 
are not so dealing, if we have irreversible changes, to 
spealx\of the pressure of the stuff is to talk nonsense ; 
to speak of a pu diagram is to tallk nonsense. He 
says (p. 71), “‘ If the common statement that the area 
of a @¢ is the same-as or proportional to that of the pu 
diagram were correct ’’ (it certainly is correct) ‘‘ there 
would be . . ., and all steam and gas engines would 
have an efficiency of (@,—8,)/@,.’? I can explain the 
meaning of this very incorrect statement only on the 
assumption that Mr. Swinburne does not know the 
cycle of a steam or gas engine. The context shows 
that he means by @, and @, (at all events in the case 
of a steam engine) the highest and lowest tempera- 
NO. 1798, VOL. 69] 
tures. Now even on the Rankine cycle of the perfect 
steam engine the above efficiency is not reached, and 
any other steam engine cycle, even if reversible, known 
to us, has a smaller efficiency that the Rankine cycle. 
I think that most of Mr. Swinburne’s mistakes arise « 
somehow from a belief that it is easy, or ought to 
be easy, to explain exactly what occurs in irreversible 
processes, and if without attacking other people he set 
himself to such a study, even so ill equipped as he 
seems to be for the task, he would have the sympathy 
of all students of thermodynamics. Most certainly it 
would be dangerous for me to criticise him, for I 
myself have given hostages to fortune in that some 
six years ago I published an attempt to study what 
occurs when steam is released from a cylinder, and the 
other irreversible operations in a steam cylinder. The 
late Prof. Fitzgerald commended my attempt, but I 
must confess that although I gave much thought to the 
matter I published it with some expressions of dissatis- 
faction. I must, however, say something about Mr. 
Swinburne’s discovery, which resembles the famous pill 
to prevent earthquakes, namely, his @x diagram. If 
@ is absolute temperature, 4.dy is the increase of energy 
““in the form of heat in the body itself.’’ Close study 
shows that he here means the heat energy received 
by the body during a small change minus the work 
done in the body’s expansion. Well, this is what we 
orthodox people call intrinsic energy dE. We may put 
it, then, in this way: if dH is the heat received by a 
body the p and @ of which are the same throughout, 
ed y=dE=dH — p.dv, 
or 
dy =dE/6=dH /0— p.dv/0. 
Now Mr. Swinburne uses a 6x diagram to show the 
changing state of the water-steam stuff, and so means 
what we mean when we say that dy is a complete 
differential. As, to Mr. Swinburne, the subject is, 
as he himself says, ‘‘ slippery,’ I would ask him to 
take no difficult case, no irreversible case, but to 
take any pv diagram of any steam engine, and 
he will find that he cannot close his cycle in a 
6x diagram. In fact, when p and v and @ and E and 
¢@ all return to their old values at the end of a cycle 
x does not do so. This happens to be a matter of 
mathematical proof, for if dH=k.dé+l.dv, Mr. 
Swinburne’s dy cannot be a complete differential 
unless 1 is equal to p. That is, the substance must be 
one the intrinsic energy of which is a function of its 
temperature only. A perfect gas has this property. 
Changing water-steam certainly does not possess it. 
If his discovery is found to be worthless in all cases 
where we have a pv diagram where we can test its 
value, why should we think it of worth for irreversible 
cases of which we know so little? 
Probably the most curious of his conflicting notions 
about entropy is what he develops in chapter iv. 
When heat is being conducted along a bar or through » 
a plate from furnace to water, he speaks of the great 
growth of entropy. It is useless to point out to him 
the importance of keeping to one definition. But 
surely even he must see that there is something quite 
inconsistent in two of his ideas. First, that if the 
state of a quantity of stuff is known, its entropy is 
known. This is, of course, a mere statement of the 
second law of thermodynamics, and he occasionally 
admits its truth. Second, a thin slice of bar which is 
conducting heat keeps in the same state all the time, 
and yet it is losing entropy continually, that is, it is 
giving out more entropy than it receives. He 
introduces a new idea quite inconsistent with his other 
ideas, that entropy is something which may’ travel 
from one body to another. He grudgingly allows us 
to tall of heat being transferred, or any kind of . 
