May 7, 1903J 



NA TURE 



1 1 



ness form the theme ; while Sparaxis heads a short 

 paragraph recording failure of growth. 



All this suggests a heterogeneous collection of 

 student's notes as the groundwork of the memoir, and 

 interesting and useful as many of these are, they might 

 have been rendered more valuable by classification and 

 efficient editing. 



The third portion of the book is occupied with general 

 considerations, and embraces summaries of the fore- 

 going, theories as to the nature of etiolation, and so 

 forth. 



Here, of course, we look for the author's own views, 

 but with the exception of vague statements here and 

 there, the concluding portions of the book force us 

 reluctantly to decide that, important and interesting 

 as the memoir is, it is so not so much as a work of 

 original thought and suggestion, but as an extensive 

 and more or less critical survey of what others have 

 done. In this category it stands well, and may be re- 

 commended, but we do not like such sentences as 

 the following exercise for the grammarian and the 

 physicist : — 



'' It is, of course, entirely probable that the action 

 of light may set up chemical processes in the plant 

 is in a manner entirely stimulative, and independent 

 of any communication or transformation of energy " 

 (p. 201). 



?ROF. ]. WILLARD GIBBS. 



THE announcement of the death of Prof. J. Willard 

 Gibbs, of Yale University, will be received with 

 the deepest regret by the whole of the scientific world. 



There are few workers who have done so much as 

 Prof. Willard Gibbs to teach the lesson that it is to 

 the mathematician that the experimentalist must look 

 for new ideas. The papers which have made his name 

 famous date from 1873, when he published in 

 the Transactions of the Connecticut Academy his paper 

 on the geometrical representation of the thermo- 

 dynamical properties of bodies. Gibbs. first discussed 

 the advantages of using different thermodynamical 

 variables for graphic representation, and then discussed 

 the surface formed by taking as coordinates the 

 volume, entropy and energy of a body. " Gibbs's 

 thermodynamical model," or " thermodynamic sur- 

 face " as it is now called, has become best known to 

 English readers through the account given in Max- 

 well's " Theory of Heat." The study of the properties 

 of thermodynamical surfaces h^s afforded a wide field 

 of research, which is still continuing to yield new re- 

 sults in the hands of the Dutch school of physico- 

 chemists. A remarkable feature of the investigation 

 is the geometric representation of the conditions of 

 thermodynamic stability, which does much to remove 

 the difficulties attaching to any algebraic form of 

 enunciation. A further paper, entitled " Graphic 

 Methods in the Thermodynamics of Fluids," was pub- 

 lished in 1878. 



Gibbs's epoch-making , papers par excellence are, 

 however, those dealing with the equilibrium of hetero- 

 tjeneous systems, the first of which, dealing with 

 chemical phenomena, was published in June, 1876, 

 while the second, dealing with capillarity and elec- 

 tricity, appeared in July, 1878. The most essential 

 feature of Gibbs's discoveries consists in the extension 

 of the notion of the thermodynamical potential to 

 mixtures consisting of a number of different compo- 

 nents, and the establishminl of lln- propcriirv thai: this 

 potential is a !inc;ir fuiiclion of (-crtaiii qLiaiuilicN 

 which Gibbs has caih^d the potentials of the com- 



ponents, and that where the same component is present 

 in different phases which remain in equilibrium with 

 each other, its potential is the same in all the phases, 

 besides which the pressures and temperatures of the 

 phases are equal. 



The importance of these results was not realised for 

 a considerable time. It was difficult for the experi- 

 mentalist to appreciate a memoir in which the treat- 

 ment is highly mathematical and theoretical, and in 

 which but little attempt is made to reduce conclusions 

 to the language of the chemist; moreover, it 

 is not unnatural to find the pioneer dwelling at con- 

 siderable length on comparatively infertile regions of 

 the newly-explored territory, while points of vantage 

 which have subsequently proved to be the most pro- 

 ductive fields of study were dismissed very briefly. It 

 was largely due to Prof, van der Waals that two new 

 and important fundamental laws were discovered ill 

 the paper, namely, the phase rule and the law of critical 

 states, and the consequences of the first of these laws 

 were the subject of remarkable developments in the 

 hands of Bakhuis Roozboom, Schreinmakers, Storten- 

 beker and Wilder Bancroft. The well-cultivated 

 tracts of knowledge which represent a most im- 

 portant branch of modern physical chemistry bear but 

 little resemblance to the crude, often circuitous path, 

 full of stumbling blocks and difficult obstacles by which 

 Gibbs first opened up this region. The study of dis- 

 sociation phenomena has afforded some of the most 

 beautiful experimental verifications of Gibbs's theories, 

 which have done much to convert theoretical chemistry 

 into a branch of applied mathematics. 



It is not the physicist and chemist alone who are in- 

 debted to Prof. Gibbs; he has also made his mark 

 among mathematicians in connection with the study 

 of quaternions and vector algebra. Physicists claim 

 that in the Hamiltonian system of quaternions there 

 is a loss of naturalness from the fact that the square 

 of a vector becomes negative. Gibbs met the objection 

 iby suggesting an algebra of vectors with a new nota- 

 ;tion, the expression for the product of two vectors 

 being formed in such a way as to give a positive value 

 ifor the square of a vector. His paper on '^ Multiple 

 I Algebra " was published in the Proceedings of the 

 j American Association for 1886. 



I Gibbs's attention has recently been turned to re- 

 i modelling the mathematical theories underlying the 

 [kinetic theory of gases, and the law of partition of 

 ^energy. His' work on statistical mcchanirs has been 

 ■before us for about a year, but so difficult is the sub- 

 ject that a considerable further time mustelapse be- 

 Ifore it can be widely understood and appreciated. His 

 interpretation of the determinantal equation as the 

 ; principle of conservation of extension in phase, his 

 •methods of dealing with ensembles of systems, and 

 this establishment of the existence of irreversible 

 phenomena in connection with such ensembles are all 

 distinct advances, but in connec;tion with the last- 

 named properties an idea necessarily forces itself on 

 one that there must be some assumption underlying, 

 the proof which niii^ht with advantage be discussed 

 more expliciily than was done in the treatise In question, 

 and his loss at the present time deprives us of the 

 prospect of further enlightenment on difficulties which 

 no amount of mere mathematical formulae will clear 

 up. 



As mentioned last week, he was elected Foreign 

 Member of the Royal Society in 1897, and received the 

 Copley medal in 190T. He was also an honorary or 

 corresponding member of the British Association, the 

 (\inibridge Philosophical Society, and many other 

 Iranicd societies both in this country and abroad. 



G. H. B. 



NO. 1749. VOL. 68] 



