i6 



NA TURE 



[May 5, 1904 



that I shall find this receptivit)' unrestricted ; and, more- 

 over, I shall reap another advantage. For I also feel 

 assured that you will offer me the severest criticism which 

 I shall be able to find anywhere. If my ideas should prove 

 worthless, they will be put on the shelf here more quickly 

 than anywhere else, before they can do harm. If, on the 

 contrary, they should contain anything sound, they will be 

 freed here in the most efficacious way from their inexact 

 and inconsistent components, so as to take the shape fittest 

 for lasting use in science. And now let us go into the 

 matter. 



The first concept we start from is equilibrium. In its 

 original meaning, this word expresses the state of a balance 

 when two loads are of the same weight. Later, the con- 

 ception was transferred to forces of all kinds, and designates 

 the state when the forces neutralise one another in such a 

 way that no motion occurs. As the result of the so-called 

 chemical forces does not show itself as a motion, the use 

 of the word has to be extended still further to mean that 

 no -variation occurs in the properties of the system. In its 

 most general sense, equilibrium denotes a state independent 

 of time. 



For the existence of such a state it is above all necessary 

 that temperature and pressure shall remain constant ; in 

 consequence of this, volume and entropy remain constant 

 too. Now it is a most general experimental law, that the 

 possibility of such a state, independent of time, is dependent 

 on the homogeneity of the system. In non-homogeneous 

 bodies, as, for instance, in a solution of 

 different concentration in different places, or 

 in a gaseous mixture of different composition 

 in different places, equilibrium cannot exist, 

 and the system will change spontaneously into 

 a homogeneous state. We can therefore limit 

 our considerations to this state, and we shall 

 consider only bodies or systems of bodies in 

 equilibrium, and, consequently, homogeneous. 



Perhaps the possibility of the existence of 

 water in contact with water-vapour might be 

 considered contradictory to this statement, 

 because we have here two different states and 

 no homogeneity. Here we meet with the new 

 concept created by Willard Gibbs, namely, that 

 of a phase. 



Systems of this kind are formed of homo- 

 geneous bodies indeed, but of more than one. 

 The water in our system is homogeneous in 

 itself, and the vapour too, and equilibrium 

 cannot exist until both are homogeneous. But 

 there is a possibility that a finite number of different homo- 

 geneous bodies can e.xist together without disturbing one 

 another. In such a system we must have the same 

 temperature and the same pressure everywhere, but the 

 specific volume and the specific entropy may change from 

 one body to the other. 



We call a phase every part of the system where these 

 specific properties exhibit the same value. It is not 

 necessary that a phase should be connected to one body 

 only ; it may be distributed over any number of parts. In 

 this way the millions of globules of butter in milk form 

 only one phase, and the watery solution of casein and 

 milk-sugar forms a second phase : milk is a two-phase 

 system. 



Every system consisting of only one phase has two degrees 

 of freedom. This law involves only the assumption that the 

 sole forms of energy involved in the system are heat and 

 volume-energy ; we exclude from consideration any effects 

 due to gravitation, electricity, surface-tension, &c. This 

 law is connected with the famous phase rule of Willard 

 Gibbs, but is not identical with it, for it contains no mention 

 at all of the so-called components of the system. Indeed, 

 the law is valid in the same way for any pure chemical 

 element, for example, oxygen, or for any mixture, for 

 example, a glass of whisky and water. If you allow to 

 the latter only one phase, it is impossible to change 

 it in more than two ways, namely, in pressure and tempera- 

 ture. 



The existence of such a body in the shape of only one 

 phase is generally limited. If the pressure be lowered at 

 constant temperature, a liquid or a solid will change at 

 last into a gas. Lowering of temperature will change a 



NO. 1801, VOL. 70] 



gas into a liquid and a liquid into a solid. For every one- 

 phase system it is possible to determine a " sphere of exist- 

 ence." This sphere is not necessarily limited on all sides; 

 for gases we do not expect a limit on the side of low 

 pressures and high temperatures, nor for solids on the side 

 of high pressures and low temperatures. But on certain 

 sides every phase has its limits, and most of these limits 

 are experimentally accessible. 



What will happen if we exceed the limit of existence of 

 a phase? The answer is most simple: a new phase will 

 be formed. The spheres of existence of the different phases 

 therefore limit one another, and the boundary-lines repre- 

 sent the interdependent values of temperature and pressure 

 for the possibility of the co-existence of both phases. 



By granting the co-existence of two phases we lose there- 

 fore one degree of freedom. At the same time a new 

 variation has arisen from the ratio between the masses of 

 the two phases. For we must not suppose that this ratio 

 is without influence on the state ; indeed we find here two 

 radically different cases. 



The most general case is, that during the transformation 

 of one phase into another the properties of both are con- 

 tinually changing, and the state of every phase is therefore 

 dependent on the ratio of the two masses. By evaporating 

 sea-water at constant temperature the density of the residue 

 grows continually higher, while the pressure, and therefore 

 the density, of the vapour goes on decreasing. It, however, 

 we evaporate distilled water, we do not find any change in 



Fig 



the properties of the residue and of the vapour during the 

 whole transmutation. 



Bodies of the first description we will call solutions, and 

 of the second, hylotropic bodies. You will be inclined to 

 call the latter substances or chemical individuals, and 

 indeed both concepts are most nearly related. However, 

 the concept of a hylotropic body is somewhat broader than 

 that of a substance. But the possibility of being changed 

 from one phase into another without variation of the proper- 

 ties of the residue and of the new phase is indeed the most 

 characteristic property of a substance or chemical individual, 

 and all our methods of testing the purity of a substance 

 or of preparing a pure one can be reduced to this one 

 property ; anyone may readily convince himself of this by 

 investigating any such method in the light of this 

 description. 



If we represent these cases by means of rectangular co- 

 ordinates, taking as abscissae the part of the first phase 

 converted into the second, and as ordinates pressure or 

 temperature, we get Fig. i for hylotropic bodies ; they are 

 represented by a horizontal straight line. With a solution 

 we get a continuous line too, but not horizontal and 

 generally not straight. If the ordinates are pressures at 

 constant temperature, and the change is from liquid into 

 vapour, the line will slope downwards as Fig. 2 shows. 

 At other temperatures the lines will be of similar shape, 

 only lying higher at higher temperatures and vice versA. 

 With other changes we obtain similar lines, sloping up- 

 wards or downwards as the case may be. For simplicity's 

 sake we will consider in the future only vaporisation ; this 

 case gives the greatest possible variety, and we are sure 

 not to omit anything by such a limitation. 



