46 



NA TURE 



[May 12, 1887 



Cavendish Professor of Experimental Physics in the University 

 of Cambridge. 



This is a continuation of a paper with the same title pub- 

 lished in the Phil. Trans., 1885, Part II. In the first paper 

 dynamical principles were applied to the subjects of electricity 

 and magnetism, elasticity and heat, in order to establish relations 

 between phenomena in these branches of physics. In this paper 

 corresponding principles are applied to chemical and quasi- 

 chemical processes such as evaporation, liquefaction, dissocia- 

 tion, chemical combination, and the like. 



Many of the results obtained in this paper have been or can be 

 obtained by means of the Second Law of Thermodynamics, but 

 one of the objects of the paper is to show that there are other 

 ways of attacking such questions, and that in many cases such 

 problems can be solved as readily by the direct use of dynamical 

 principles as by the Second Law of Thermodynamics. 



A great deal has been written on the connexion between the 

 Second Law of Thermodynamics and the principle of Least 

 Action ; some of these investigations are criticised in the first 

 part of the paper, after this it is shown that, for a collection of 

 molecules in a steady state, the equation (which for ordinary 

 dynamical systems is identical with the well-known Hamiltonian 



principle) — 



S{T-V) = o, 



is satisfied ; where T and V are respectively the mean values of 

 the kinetic and potential energies taken over unit time, and 

 where the variation denoted by 5 is of the following kind. 



The co-ordinates fixing the configuration of any physical 

 S3^tem, consisting according to the molecular theory of the 

 constitution of bodies of an immense number of molecules, may 

 be divided into two classes : — 



(«) Co-ordinates, which we may call molar, which fix the con- 

 figuration of the system as a whole ; and 



{b) Molecular co-ordinates which fix the configuration of in- 

 dividual molecules. 



We have the power of changing the molar co-ordinates at our 

 pleasure, but we have no control over the molecular co-ordinates. 



In the equation — 



S(f-V) = o, 



only the molar co-ordinates are supposed to vary, all velocities 

 remaining unchanged. Hence in applying this equation we 

 need only consider those terms in T and V which involve the 

 molar co-ordinates. Expressions for these terms for gases, 

 liquids, and solids are given in the paper ; the rest of the paper 

 after these have been obtained consists of applications of the 

 above equation. 



The density of a vapour in equilibrium with its own liquid is 

 obtained as a function of the temperature, and the effect up on 

 the density of such things as the curvature or electrification of 

 the surface of the liquid is determined. 



The phenomenon of dissociation is next investigated, and an 

 expression for the density of a dissociated gas obtained which 

 agrees substantially in form with that given by Prof. Willard 

 Gibbs in his well-known paper on the "Equilibrium of Hetero- 

 geneous Substances." 



The effect of pressure upon the melting-point of solids and 

 the phenomena of liquefaction are then investigated, and the 

 results obtained for the effect of pressure upon the solubility of 

 salts are shown to agree with the results of Sorby's experiments 

 on this subject. The effect of capillarity upon solubility is in- 

 vestigated, and it is shown that if the surface-tension increases as 

 the salt dissolves then capillarity tends to diminish the solubility, 

 and vice versd. 



The question of chemical combination is then considered, 

 particularly the results of which is called by the chemists 

 " mass-action," and of which a particular case is the division of 

 a base between two acids. 



The general problem investigated is that in which we have 

 four substances. A, B, C, D, present, such that A by its action 

 on B produces C and D, while C by its action on D produces A 

 and B. The relation between the quantities of A, ^B, C, D 

 present when there is equilibrium is obtained and found to 

 involve the temperature ; when the temperature is constant it 

 agrees in some cases with that given by Guldberg and Waage, 

 though in others it differs in'some important respects. Thus, if 

 {> n, C) « be the number of molecules of A, B, C, D respectively, 

 when there is equilibrium, the absolute temperature, H the 

 amount of heat given out when the chemical process which 



results in the increase of | by unity takes place, and k a quantity 

 which is the same for all substances, then it is proved that — 



where C is a constant ; /, q, r, s are quantities such that if (A) 

 represents the molecule of A, with a similar notation for the 

 other molecules, tlien the chemical reaction can be represented 

 by the equation — 



J>{A} + g{B}=r{c} + s[D}. 



Thus if A, B, C, D be respectively sulphuric acid, sodium 

 nitrate, nitric acid, and sodium sulphate, in which case the re- 

 action is represented by — 



H.^S04 + 2NaN03 = aHNOj + NaaSOj, 



then, if the molecules of sodium nitrate and nitric acid be 

 represented by NaNOg and HNO3 — 



p — I, q = 2, ^ = 3, and s = I, 



If, however, the molecules of sodium nitrate and nitric acid 

 are represented respectively by NagNjOg and HjNgOg, ther 

 since the chemical reaction may be written — 



H,S04 + Na2N206 = H2N206 + Na.,S04, 

 p ~ \, ^ = I, r - \, and 5=1. 

 According to Guldberg and Waage the relation between |, r;, 

 C» e is— 



!>? = K^ ; 



this, when the temperature is constant, agrees with the above 

 expression \i p = q = r — s. 



We see that the state of equilibrium will vary rapidly with 

 the temperature if H be large, that is, if the chemical process is 

 attended by the evolution of a large quantity of heat. 



The effect of alterations in the external circumstances such as 

 those which may be produced by capillarity, pressure, or electri- 

 fication are investigated, and it is shown that anything giving rise 

 to potential energy which increases as the chemical combination 

 goes on tends to stop the combination. 



The last part of the paper is taken up with the consideration 

 of irreversible effects such as those accompanying the passage of 

 electric currents through metallic conductors or electrolytes. 

 These are looked upon as the average of a large number of dis- 

 continuous phenomena which succeed each other with great 

 rapidity. The ordinary electrical equations with the usual re- 

 sistance terms in, represent on this view the average state of 

 the system, but give no direct information about its state at any 

 particular instant. It is shown that if we take this view we can 

 apply dynamical principles to these irreversible effects, and the 

 results of this application to the case of electrical resistance are 

 given in the paper. 



" On Parts of the Skeleton of Meiolania platyceps." By 

 Sir Richard Owen, K.C.B., F.R.S. 



The subjects of the present paper are additional fossil remains 

 of Meiolania platyceps from Lord Howe's Island, transmitted to 

 the British Museum since the author's previous paper on that 

 extinct reptile. Additional cranial characters are defined and 

 illustrated by drawings of more or less perfect specimens of the 

 skull, of vertebrze of the neck, the trunk, and tail, of limb-bones, 

 and portions of the dermal skeleton. 



The author sums up the affinities, deducible from the above 

 parts of the skeleton, to the orders Chelonia and Sauria, with 

 grounds for the conclusion, mainly based on the absence of 

 evidence of a carapace and plastron, that the genera Megalania 

 and Meiolania are more nearly akin to the Saurian division of 

 the class Reptilia ; in which he proposes to refer those extinct 

 genera to a sub-order called Ceratosauria. 



"Conduction of Heat in Liquids." By C. Chree, B.A., 

 King's College, Cambridge. Communicated by Prof. J. J. 

 Thomson, F. R. S. 



Linnean Society, April 21. — Mr. W. Carruthers, F.R.Sv,: 

 President, in the chair. — Mr. E. M. Holmes exhibited speci- 

 mens of various species of Shorea from Borneo and Sumatra, 

 which plants yield vegetable fats used for teclinical purposes. 

 Several species of Dichopsis affording gutta-percha from the bark 

 and fat from the seeds were also shown. Mr. Holmes pointed 

 out the importance of the cultivation of the more valuable of 

 these trees, among others, D. oblongifolia and Ceratophorus 



