We have seen above that the total fraction found transformed when a reaction is over de pends, among other things. on the masses present at its beginning. Similarly, it may be demon strated by facts that the fraction transformed in a given interval of time during the reaction depends on the masses present at the beginning of that interval. And since the reaction itself obviously changes the masses present, part of the original substances gradually disappearing as such and masses of the products of the reac tion gradually appearing in their stead, it is evident that the magnitude of the) fraction transformed in unit of time varies from instant to instant. Were this not so, the 'velocity' of a chemical reaction might be defined in terms of the amounts found transformed in any finite interval of time. But since, as just explained, the velocity is variable, it can be defined only in terms of the infinitely small amounts trans formed in infinitely short intervals of time. (If this does not seem clear, see the article CAL ctaxs.) It may, however, be asked: But why consider at all the velocity of reactions? The answer is, Because it is the velocity that is immediately determined by affinity and mass action; and so, conversely, it is by measuring the velocity that affinity and mass action can be studied quantitatively. In the case of a re versible reaction, the direction of the change is the direction in which the velocity of reaction is the greater; the amount actually found trans formed in any time depends on the difference between the velocities with which the two op posite reactions take place; and when the two velocities are equal, there is equilibrium. Thus the velocities of a reaction describe its course completely.
The development of the principles discussed in the precedidg paragraphs forms the object of chemical kinetics and statics, the two sub divisions of the modern 'doctrine of affinity.' Chemical kinetics deals with chemical change: chemical statics with chemical equilibrium. At the basis of both is the law of mass action in its precise mathematical form, which may now be considered as established beyond the slightest possibility of doubt. For it has been demon strated in three different ways: (1) by mathe matical deduction from the kinetic theory of gases; (2) by mathematical deduction from the laws of thermodynamics; and (3) by extensive experimental observation. Correctly, but vague ly. the action of masses was first understood by the Frenchman Berthollet. in the beginning of the nineteenth century. In 1867 Guldberg and Waage, two Norwegian investigators, published a work (Etudes sur les affinitcls chimiques) in which the principles of chemical statics and kinetics were first stated and demonstrated in their rigidly mathematical form. But this work remained unknown for a number of years. Mean while Van't Hoff discovered the law of mass action independently in 1877; and from this date may be said to commence a new epoch in theo retical chemistry. The principal names con nected with the demonstration and mathematical and experimental development of the law are. besides those of Guldberg and Waage. the names of Van't Hoff, Horstmann, Gibbs, Arrhenius. and Ostwald.
For further information, consult the works on theoretical and physical chemistry recommended in the article CHEMISTRY. See also A ems: DE COMPOSITION; DISSOCIATION; ELECTRO-CHE3I ISTRY ; ESTERS ; SOLUTION ; THERMO-CHEMISTRY.