54 



NA TURE 



[May 19, 1904 



north, in the region of the prairies. Moreover, even if the 

 natives had known, the horse, they jnight well have been 

 astonished at the Jiorse-and-man combination.' Then it is 

 difficult to understand why Equus became totally extinct, 

 since subsequent events showed that vast areas were admir- 

 ably adapted to it. Prof. Ewart informed me (ii(i. 1902) 

 that the Chinese were alleged to have visited America about 

 the eleventh century, and reported it as the " land of women, 

 the horse and the vine." This tradition is apparently not 

 to be regarded very seriously, but the antiquity of the 

 genuine Equus caballus in North America is supported by 

 O. P. Hay in his excellent catalogue of the fossil 

 Vertebrata of North America (1902), p. 622. This author 

 boldly lists E. caballus as Pleistocene on this continent, and 

 while admitting that " in some cases the identifications have 

 been open to question," and " in other cases the remains 

 may have been derived from the introduced race," he adds, 

 " the former existence of the species in Alaska and in 

 California appears well established." Of course, the term 

 E. caballus must here be understood in the wider sense. 

 Prof. Ewart also remarked, in the letter just cited, that the 

 Spaniards at the time of the conquest used small-headed 

 horses, " the offspring of the E. fossilis of Asia in all prob- 

 ability," whereas the characteristic " buckskin " pony of 

 our south-west is a relatively large-headed animal. Further- 

 more, Mr. Wilfred Blunt, 'through my brother, Mr. S. C. 

 Cockerell, communicated the statement that " the Spaniards 

 never rode mares, and can hardly have brought any but 

 stallions with them in their ships to their colonie.s." Hence 

 the early abundance of wild horses in North and South 

 America appears very remarkable. With reference to the 

 presumed early absence of horses, one may also remark that 

 so common an animal as the " antelope " (Antilocapra) 

 was not made known to naturalists until about 1815, and 

 a perfectly new wild sheep was discovered in northern 

 Mexico in 1901 ! Even the known variability in colour of 

 the wild horses might be thought of as a Mendelian pheno- 

 menon, resulting from the mixture of different types, and 

 the infusion of new blood could be conceived to have re- 

 sulted in greater vigour and consequent increase in numbers. 

 T. D. A. Cockerell. 

 Colorado Springs, Colorado, U.S.A. 



This paper, only slightly abridged and with about one- 

 third of the figures, appeared in Nature of April 21 (vol. 

 Ixix. p. 590). I am more than " half inclined to regard the 

 Celtic pony as a valid species " and to recognise three species 

 of living horses. I prefer, however, to leave systematists 

 to decide whether Prjevalsky's horse and the Celtic pony 

 should be regarded as species or merely as varieties. 



J. C. E. 



Entropy. 



An author expects some unfavourable reviews, and, if 

 wise, profits largely by them ; but Prof. Perry's review of 

 " Entropy " in Nature of April 14 is simply an attempt to 

 brush away a book the object of which is to eradicate 

 what, I submit, is a very widespread mistake, because the 

 reviewer has himself not only made the mistake, if mistake 

 it be, but championed it. This mistake is that entropy is 

 conservative in irreversible change ; that the entropy of a 



body is increased only by its taking in heat, or that f dH/e 



is the entropy in irreversible change ; or that dH/e is a 

 complete differential. In Prof. Perry's own words, " There 

 is a property of the stuff called its entropy <^, which is such 

 that any change in it, 5^ if multiplied by ( the absolute 

 temperature gives 5H or 8H = (5i^." " ip is to heat re- 

 received H something like what v is to work to." " If we 

 divide every 5H by (, . . . every amount 5H being divided by 

 the t at the time, and if we call 5H divided by Ae t by the 

 name, entropy, we shall find that when the stuff is brought 

 back to its old state again, we have just given out as much 

 entropy as we have taken in. The account balances 

 exactly." 



In a note to a presidential address I pointed out that 

 such statements are numerically correct in reversible changes 

 1 Some of the aboriginal pictographs ihow horses, but these are ap- 

 parently of recent date. Unfortunately we have no ancient American 

 drawmgs of animals comparable to those of Europe. 



NO. 1803, 'VOL. 70] 



only, that in all irreversible changes they are not accurate, 

 and that they thus give a wholly wrong idea of the function 

 entropy. There was no question, and never has been, about 

 reversible changes, that is to say, changes where p and d 

 are uniform throughout the working .substance ; the whole 

 of my criticism refers to irreversible changes alone. 



Prof. Perry then started a correspondence in which Prof. 

 Poincar^ and Prof. Planck were good enough to join, and 

 also showed how Prof. Perry was wrong {Electrician, 

 March 13, 1903). I quote from Prof. Planck's letter: — 



" The controversy excites my attention the more, when, 

 to my astonishment, I see a man so well known and so 

 eminent in science as Sir Oliver Lodge ' putting forward 

 ideas on thermodynamics {Electrician, January 23, p. 460) 

 which I combated ever since the commencement of my 

 studies in that science." 



" But how can I hope with my words to make any im- 

 pression on such writers when Mr. Swinburne's excellent 

 articles have failed to effect any change in their preconceived 

 ideas? For, with one reservation," what he has written in 

 the Electrical Review (January g, p. 52) is, in my opinion, 

 one of the best and clearest expositions of the subject that 

 has ever been written, especially where he points out that 

 Nature never undertakes any change unless her interests are 

 served by an increase of entropy, while man endeavours so 

 to make use of those changes allowed by Nature that his 

 own interests — namely, the acquisition of available energy 

 — are served as completely as possible." 



Science can never be a matter of authority, but I quote 

 Prof. Planck because Prof. Perry now reviews the book 

 as if his definition of entropy was universally accepted in 

 thermodynamics, and adopts the tone that anyone who 

 differs from himself and develops Clausius's inequality, 



jdH/6<-tl> for all irreversible changes, is wrong prima 



facie. 



Though the review contains quotations from the little 

 book, they are always incomplete, so as to give as far as 

 possible an absurd meaning. Thus the quotations about 

 errors in text-books look as if I said text-books on thermo- 

 dynamics are wrong. What I do say is that books on 



physics and steam engines define ^ as jiH/9, whereas 



books on thermodynamics show that is accurate for re- 

 versible changes only. The whole gist of my book is the 

 application of Clausius's principle of increase of entropy. 

 Books on steam engines, and generally on physics, as 

 opposed to those on thermodynamics, say d<f> =dH/9, and 

 dll/O is a complete differential. If means the temperature 

 of the working substance when that temperature is not 

 uniform, dH/d has no meaning, and is not a complete 

 differential. By 6 in irreversible change, as I have often 

 explained, I mean the temperature at the separating surface 

 through which dH passes. If no meaning can be given to 

 dH/9 in irreversible change, my criticism that dH/e is not 

 a complete differential, except in the ideal case of reversi- 

 bility, is still valid. " It is hardly believable that in a 

 dynamical illustration he should imagine the momentum 

 of a system of two colliding bodies to be increased by the 

 collision " is calculated to give the impression that I am 

 ignorant of elementary mechanics. The context is dis- 

 cussing the sum of the scalar momenta of gas particles-. 

 This increases when some isolated gas equalises its tempera- 

 ture at constant volume. " But as we have the foot-pound, 



1 The reference to Sir Oliver Lodge occurs because he wrote an article 

 on entropy defined so that H ^Jedifi, which I take it he has recalled. It 

 was because I thought the weight of his authority might tell harmfully that 

 I sent the correspondence to two leading authorities on thermodynamics. 



- This was my statement that d'j, is never a complete differential in 

 irreversible change. For (/.(> to be a complete differential in terms of say, 

 M, rfe, we must have rf* = Mde+Ndv, where 3M/flr. = gN/3«. To prove 

 rfij> a perfect differential during any irreversible change the equation must 

 be true while the change is going on. It is not accurate to put the value of 

 9 or of/ which obtained before the change started, or would he reached if 

 the change were arrested and the substance allowed to come to uniform 

 temperature and pressure. Prof. Planck is so much better a physicist and 

 mathematician than 1 am that I do not contradict such an authority; I 

 merely say there is a misunderstanding, which may be mine, and I 

 submit my contention. My view is that the physical meaning of a 

 complete differential in mechanics is not only that the integral is completely 

 determined by the coordinates, but that it is conservative. Lagrange's 

 treatment of mechanics re.^lly involved the conservation of energy, that is 

 to say of the forms he discussed. 



