August 12, 1922J 



NA TURE 



207 



volume contains a great many useful observations 

 and a very lucid and stimulating review of the subject. 

 One may question whether the biological influences 

 have quite the dominating importance in the soil 

 that is here claimed for them, and in particular whether 

 the organisms found in it can as yet be satisfactorily 

 used as a criterion of the agricultural properties of a 

 soil ; but the subject is still young and its possibilities 

 are undoubtedlv great. 



Planck. Sechste Auflage 



W. De Gruyter und Co., 1921.) 



ONE of the most universal generalisations that can 

 be made about the study of mathematical 

 physics is that everybody finds thermodynamics a very 

 difficult subject. In consequence of this there have 

 arisen several different ways of presenting it, which 

 vary far more from one another than do the presenta- 

 tions in such subjects as dynamics or electricity. 

 There is first the thermodynamics of the engineer, in 

 which entropy is something steam has, which can be 

 found from tables. Then there is the thermodynamics 

 of the chemist, whose laboratory is stocked with semi- 

 permeable membranes. He is a great designer of 

 engines, but all his enjoyment of his wonderful instru- 

 ments is spoiled by his perpetual suspicion that Nature 

 is trying to score off him. Next, there is the thermo- 

 dynamics of the mathematician ; this scraps the 

 chemist's machinery and does the whole business by 

 means of Pfaffian forms, a peculiar branch of mathe- 

 matics, and almost the only one in which it looks as if 

 more comes out at the end than is put in at the begin- 

 ning. Lastly, there is the super-man. who can see and 

 count the atoms, who regards all the others as gamblers, 

 though he is bound to admit that they know how to lay 

 the odds. He occupies a position rather apart, being, 

 so to speak, engaged in a study of the jurisprudence of 

 thermodynamics. 



Xuw (excepting the last), all these presentations 

 claim to derive their results from the two laws of 

 thermodynamics, but there is no agreed statement of 

 those two laws. In most books the chapter on the 

 Second Law is not opened by a formal statement of 

 that law — as Newton's laws of motion would head the 

 corresponding chapter in a book on dynamics — but 

 it is necessary to have several pages of tendencious 

 discussion first, to create the atmosphere in which the 

 law shall be acceptable. This can only mean that the 

 law as stated contains a good many implied assump- 

 tions. Some years ago Caratheodory, the pure 

 mathematician, formulated the principles in a really 

 NO. 2754, VOL. 1 IO] 



The Presentation of Thermodynamics. 

 Vorlesungen iiber Thermodynamic. Von Prof. Dr. Max 



Pp. x + 292. (Berlin : | bv temperature in the presentation. In the ordinary 

 way it occurs muddled up with the Second Law, but 



logical manner, and it is to be hoped — if we can believe 

 that the human mind is by taste rational— that this 

 formulation will be more successful in making the 

 subject easy than has the exceptional variety in 

 presentation which has hitherto prevailed. Cara- 

 thcodory's work was transcribed a year or two ago 

 in the Physikalische Zeitschrift by Born. He insists 

 that there is no way of shirking the Pfaffian problem 

 in some form or other, but gives a simple geometrical 

 description of it ; in the consequent deduction of 

 absolute temperature and entropy there is some rather 

 heavy work which could probably be simplified. But 

 the most important modification is the new place taken 



here it is taken out and introduced as the primitive 

 idea — of course, measured on an arbitrary scale. The 

 consequence is that the First Law no longer deals with 

 quantities which are undefined, and the Second Law 

 becomes a clear-cut statement instead of a jumble of 

 two statements. 



The new presentation is too recent to have been 

 adopted in text-books, and it will be most interesting 

 to see whether it is destined to drive out the older 

 types. The book under review is of a class about mid- 

 way between those of the chemist and those of the 

 mathematician. That it has gone through six editions 

 shows that it is a first-rate introduction to the subject ; 

 but it certainly can be criticised from the logical point 

 of view, for it brings in absolute temperature by means 

 of the perfect gas, and only later justifies it in the 

 general case. It is a philosophical question whether 

 it is legitimate to introduce ideas connected with reality 

 by means of a hypothetical substance— perhaps it 

 may be defended, like the introduction of rigid bodies 

 in dynamics. But the point really is that this method 

 is apt to leave the student with the idea that absolute 

 temperature is in some way connected with perfect 

 gases, an idea rather encouraged by many of the 

 examples that are usually cited. It is surely a pity 

 to start by dealing with a special case, when 'the whole 

 argument is that Carnot's cycle works exactly as well 

 whatever the substance in the cylinder. Apart from 

 this criticism, however, the whole work is an admirably 

 detailed development of the theory, with numerous 

 illustrative examples from physical chemistry. The 

 chief changes in the new edition are in connexion with 

 the theory of solutions ; in particular, an account is 

 given of the theory of J. C. Ghosh of Calcutta, of the 

 freezing-points of strong solutions, which would seem 

 to have attracted more attention in Germany than in 

 this country. There is also more said about the 

 equation of state of solids and their expansion co- 

 efficients. 



