Real and Apparent Equilibrium.--In discussing equilibria, also, a distinction must be drawn between real and {6} apparent equilibria. In the former case there is a state of rest which undergoes continuous change with change of the conditions (_e.g._ change of temperature or of pressure), and for which the chief criterion is that _the same condition of equilibrium is reached from whichever side it is approached_. Thus in the case of a solution, if the temperature is maintained constant, the same concentration will be obtained, no matter whether we start with an unsaturated solution to which we add more solid, or with a supersaturated solution from which we allow solid to crystallize out; or, in the case of water in contact with vapour, the same vapour pressure will be obtained, no matter whether we heat the water up to the given temperature or cool it down from a higher temperature. In this case, water and vapour are in _real_ equilibrium. On the other hand, water in contact with hydrogen and oxygen at the ordinary temperature is a case only of _apparent_ equilibrium; on changing the pressure and temperature continuously within certain limits there is no continuous change observed in the relative amounts of the two gases. On heating beyond these limits there is a sudden and not a continuous change, and the system no longer regains its former condition on being cooled to the ordinary temperature. In all such cases the system may be regarded as undergoing change and as tending towards a state of true or real equilibrium, but with such slowness that no change is observed. Although the case of water in contact with hydrogen and oxygen is an extreme one, it must be borne in mind that the condition of true equilibrium may not be reached instantaneously or even with measurable velocity, and in all cases it is necessary to be on one's guard against mistaking apparent (or false) for real (or true) equilibrium. The importance of this will be fully illustrated in the sequel. * * * * * {7} CHAPTER II THE PHASE RULE Although the fact that chemical reactions do not take place completely in one direction, but proceed only to a certain point and there make a halt, was known in the last quarter of the eighteenth century (Wenzel, 1777; Berthollet, 1799); and although the opening and subsequent decades of the following century brought many further examples of such equilibria to our knowledge, it was not until the last quarter of the nineteenth century that a theorem, general in its application and with foundations weakened by no hypothetical assumptions as to the nature or constitution of matter, was put forward by Willard Gibbs;[5] a generalization which serves at once as a golden rule by which the condition of equilibrium of a system can be tested, and as a guide to the similarities and dissimilarities existing in different systems.