June 27, 1901] 



NA ruRh 



aires and the Zciischrift fiir physikalische C/ieiiiie, and, 

 secondly, later developments and additions and the 

 application to recent experimental work, most of which 

 was carried out by Prof. Kamerlingh Onnes and his 

 pupils at Leyden. \'an der Waals pays an eloquent 

 tribute to Prof. Onnes' merits in this direction in the 

 dedication of this second volume. It appears that but 

 for him the original theory might never have been pub- 

 lished and would certainly not have borne any fruit. 



The importance of a theory of mixtures, as of other 

 theories, lies in this, that it may show the connection 

 between a number of phenomena which otherwise have 

 to be treated separately, and may, directly or indirectly, 

 bring to light new ones. That a theory was urgently 

 wanted in the phenomena of mi.xtures even of two sub- 

 stances need not be set forth. In a theory of mixtures 

 we may distinguish different parts, more or less inde- 

 pendent of each other, which together form the whole. 

 It consists firstly of an application of thermodynamics to 

 find out the rules for the coexistence of phases — the gas 

 and the one or two liquids. To do this it is only necessary 

 to assume the experimental fact that the properties of 

 mixtures form a continuous series between those of the 

 components and, therefore, that a mi.xture has an equation 

 of condition of the same general features as that of a 

 single substance. Van der Waals is not the only man 

 of science who has been working on these lines, although 

 doubtlessly the first who conceived the notion of such a 

 theory. Not only had special problems relating' to mix- 

 tures been successfully treated by Konowaloff and others, 

 but Duhem, applying his method of the thermodynamic 

 potential, had been working in the same direction. In the 

 reviewer s opinion, however, it cannot well be denied that 

 the method used Ijy van der Waals in attacking the pro- 

 blem by means of the " free energy" ^, and it5 graphical 

 representation, is by far the most effective and the safest 

 guide amidst the intricacies of the problem. 



Leaving alone questions of priority, we may say that 

 the theory as sketched has led, more or less directly, to 

 the complete disentanglement of the critical phenomena 

 of mi.xtures, to the tracing of the proper features of the 

 various diagrams between the pressure, volume, tem- 

 perature and composition, and to the discovery of various 

 other new facts, such as the existence of maxima and 

 minima in the critical temperature and their connection 

 with minima and maxima in the vapour pressure, and 

 the influence of pressure on the coexistence of two 

 liquids. All these and many other points are fully set 

 forth by van der Waals in this second volume. 



V'an der Waals has not, however, contented himself 

 with that ; from molecular considerations he was able to 

 deduce an equation of condition for mixtures of a definite 

 form, depending, as does his well-known formula for 

 single substances, on attraction-constants n and volume- 

 constants b. It is somewhat to be regretted that in the 

 original paper no attempt was made to guide the reader 

 in ascertaining in how far special results arrived at were 

 dependent upon this special equation or not ; everybody 

 will feel the importance of the distinction, and certain 

 controversies which have arisen in connection with the 

 theory would have been prevented by a clearer distinction 

 on this head. 



The importance of this point has increased lately in 

 connection with the modern conception of normal (non- 

 associating) and abnormal (associating) substances. \'an 

 der Waals' equation can be used for normal substances 

 as an approximate guide, although even for these the 

 approximation is veiy rough and hardly amounts to more 

 than a certain resemblance, at least at small and medium 

 volumes. For abnormal liquids the equation cannot 

 even profess to do that, and van der Waals' results, 

 in so far as they depend upon this equation, are not 

 applicable to these substances at all. Lehfeldt has 

 noticed that, so far as we know, normal liquids mix in all 

 NO. 1652, VOL. 64] 



proportions and that partial miscibility occurs when at 

 least one of the components is abnormal. \'an der 

 Waals' theory does not confirm this, inasmuch as such 

 values may be assigned to the constants in his equation 

 as will lead to partial miscibility. At the same time, as 

 no normal liquids of partial miscibility have been dis- 

 covered so far, this subject is outside the scope of van der 

 Waals' equation. 



The reader must not get the impression that results 

 deduced for normal liquids by means of van der Waals' 

 equation are of small value ov^ing to the inaccuracy of 

 the equation. An instance will illustrate this. Van der 

 Waals discusses the question, also treated by Ostwald 

 and others, what function of the composition of a mixture 

 its vapour-pressure is. He arrives at certain conclusions, 

 one of which is that there cannot be more than one 

 maximum or minimum, at least that the combination of 

 a maximum and a minimum is very unlikely. Guided 

 by this result, Hartman (Leyden) has discovered that 

 there is an obvious error in Konowaloff's result for pro- 

 pionic acid and water, the curve for this combination 

 being in contradiction to Konowaloffs own measurements, 

 and Kohnstamm, working in van der Waals' laboratory, 

 similarly discovered an error in Linebarger's result for 

 benzene and carbon tetrachloride, a result which, if it 

 had been confirmed, would have been even more striking,, 

 as both these substances are normal. On the other 

 hand, Caubet and Duhem maintain to have realised 

 the double phenomenon in question with methyl chloride 

 and sulphur dioxide ; if the latter result were confirmed 

 it would certainly show in a striking way with what 

 extreme caution conclusions drawn from the approximate 

 theory have to be accepted. 



Owing to the recent establishment of a "van der 

 Waals fund,'' the famous author is now in a position 

 to conduct experimental researches in his own labora- 

 tory. Several valuable memoirs have already appeared 

 under this trust. 



A very interesting departure has been lately made by 

 Kamerlingh Onnes and his pupils to construct plaster 

 models of the -^ surface entirely based on experimental 

 data. Models of that kind will no doubt become a 

 powerful assistance in the understanding of the intricate 

 phenomena displayed by mixtures. 



Turning our attention towards the work which is being 

 done in the Leyden laboratory, we notice researches 

 which are being carried on relating to Hall's phenomenon,, 

 the magnetic rotation of the plane of polarisation and 

 many others. A special feature of the work is the con- 

 stant use of low temperatures down to the boiling point 

 of air. We feel at a loss what particular part of the 

 work to review specially ; in the small space available 

 no justice could be done to any one without being un- 

 just to others, and we abstain from reviewing anything 

 in particular, considering that the " Communications- 

 from the Physical Laboratory at Leiden" are widely 

 distributed and will, no doubt, be sent to anybody 

 interested who takes the trouble to apply for them. 



Much else might have been mentioned in this review, 

 but we have tried to select that which would find the 

 largest number of interested readers. J. P. K. 



MAXIME CORNU. 

 'T'HE hand of death has been heavy on the French 

 ■* botanical world. In recent years it has fallen 

 successively on Duchartre, Baillon, Naudin, de Vilmorin 

 and Franchet : all men in the foremost rank, whom their 

 fellow-workers in England counted as sympathetic 

 friends. And now the untimely and unexpected death 

 of Maxime Cornu has come upon many of us — and not 

 least at Kew — as a personal grief. I saw him last 

 autumn in Paris full of the business of congresses into 

 which he was throwing himself with irrepressible vivacity 



