Acetamide was employed; the experiments were made at 65° and 100°, for intervals of time varying from 2 minutes to 50 days. The amounts of chemical change, for given intervals of time, at a constant temperature, are determined and tabulated for each acid employed; then, by the use of an interpolation-formula, the time is found which is required by each acid to accomplish 50 per cent. of the total change; and lastly, by dividing the intervals of time in the first table by the times required for the half-completion of the process, comparable numbers are obtained which express the amount of change effected by each acid in the same time. Putting the velocity as inversely proportional to the time required for reaching a determinate stage of the decomposition, it is shewn that the ratios of the velocities of different acids are not constant, but depend on the stage of the operation selected. Ostwald, as we have seen, selects the stage at which the operation is half completed; the velocities are stated in terms of that of hydrochloric acid taken as 100. A curve theoretically representing the progress of the change is constructed by help of the formula = ν a- -y = Ct, where y amount of acid decomposed in time, the active mass of which acid at the beginning of the reaction is represented by a, and C a constant. = This equation is obtained by developing the fundamental equation given by Guldberg and Waage1, v=$(T− T); it therefore assumes the correctness of the law of mass-action formulated by these naturalists, and also that the substances formed during the reaction exert no influence on the process. The actually observed results are plotted alongside the theoretical curve; the curves representing the process at 65° and 100° are nearly identical. A comparison of the curve calculated by the formula, with the results plotted alongside, shews that the process is not entirely free from secondary reactions. Among these secondary reactions are to be placed the influence of the neutral ammonium salts of the monobasic acids (see ante, par. 220), the influence of the acid ammonium salts of the polybasic acids, and the probable formation of amido-acids in the case of trichloracetic acid, &c. Nevertheless, the numbers obtained are comparable with those arrived at by Ostwald's former equilibrium-studies, inasmuch as the secondary changes in both series of reactions are very similar'. 223. In a former paper it had been shewn by Ostwald, that when equilibrium is established by the competition of two acids for the same base, the factors k and k' in Guldberg and Waage's fundamental equation, may with great probability be resolved each into two parts, one dependent on the nature of the base, and the other on the nature of the acids. Treating k and k' in this way, he gets where a and a depend on the nature of the acids, and ẞ on 1 For details see Ostwald, loc. cit. (2) 27. 24 and 31. 2 For further discussion see Ostwald, loc. cit. (2) 27. 24―31. 3 loc. cit. (2) 16. 422. See also post, par. 227. that of the base, c being a constant. Hence a and a depend (probably) only on the nature of the acids, and measure their affinities, it follows that the values of these affinities are as the square roots of the velocities of the reactions wherein the acids take part1. The relative affinities of the various acids employed in this investigation are then calculated from the observed velocities, that of hydrochloric acid being taken as 100. The results agree very fairly with those formerly obtained (see post, par. 235). It is to be remembered that both series of numbers are affected by the occurrence of secondary changes in the chemical operations from the study of which they were deduced. We have already learned (ante, chap. II. par. 187) that the molecular theory of chemical action points to a close connection between the rates at which chemical changes proceed, and the affinities (using this term in a wide sense) of the reacting bodies. This connection is now seen to be emphasised, and rendered exact, by the more purely dynamical studies based on Guldberg and Waage's theory of affinity2. 224. These studies are continued, with similar results, in Ostwald's next paper, where the operation represented by the equation CH,. COOCH,+HOH=CH,. COOH + CH3. OH is selected for investigation, as being simple, and also typical3. The change proceeds at different rates in the presence of different acids. The action of the acids belongs to the class known as contact or catalytic actions (see ante, chap. II. par. 178). Ostwald has carefully examined this process, using various acids, varying the time of action, &c., and has convinced himself that the operation is in all cases of the same kind, 1 For a fuller treatment of this part of the subject see Ostwald, loc. cit. (2) 27. 35-36. 2 We have here an instance of the merging into one, of the two paths of chemical advance. 3 loc. cit. (2) 28. 449. and that the same formula for finding the amount of methylic acetate decomposed may always be used, viz. where a amount of acid, b = amount of ethereal salt at the beginning of the reaction, and x = amount of this salt decomposed in time t, c being a constant1. The action is completed and equilibrium established in 24 hours; it is not however always necessary to carry the process to this final state, inasmuch as it can be shewn (and this is verified by experiment) that the final state is reached after a period ten times as long as that during which 50 per cent. of the ethereal salt is decomposed. 225. Having thus satisfied himself as to the general character of the reaction which occurs in the catalytic decomposition of methylic acetate by acids in presence of water, Ostwald proceeds to study the influence exerted on the velocity of the change by varying the acids employed. His results are tabulated (pp. 472-486) and the square roots of the different velocity-coefficients are given in terms of that of hydrochloric acid as 100. The affinities of the acids as thus obtained are represented by larger numbers than those arrived at by the use of equilibrium-methods (see table loc. cit. p. 487; also post, par. 235). But this apparent increase in the values of these affinities is shewn to be due to secondary actions, between methylic acetate and water, which occur in the process in question. Nevertheless, the two series of numbers exhibit the closest parallelism even in small details. 226. In a later communication, Ostwald shews that the 'inversion' of cane sugar in presence of various acids follows the same course as the change of methylic acetate into alcohol and acid. He employs the formula already given, viz. 1 See loc. cit. (2) 28. 451-472 for details regarding this formula and the ways in which Ostwald has tested its validity. 2 loc. cit. (2) 28. 452-453. 3 loc. cit. (2) 29. 385. The quotient obtained by dividing these values by the time of action should be a constant quantity; this constant, c = b = log constant. b x /a.t., Ostwald calls the inversion- (or velocity-) The results shew that the observed variations in the values of this quantity are very small, and are such as may be fairly attributed to errors of experiment (loc. cit. p. 401). The square roots of the velocity-constants represent the relative affinities of the acids employed. The numbers obtained from this investigation agree very closely with those deduced from the experiments with methylic acetate; see table, par. 235. In this paper Ostwald gives a table shewing the for all values of between values of log b I , or log x x O'001 and 0.999, to facilitate the calculations of those who may investigate the velocity-constants of various reactions. 227. From all these researches, Ostwald concludes that each acid, and each base, possesses a specific affinity-constant; and that all the chemical reactions in which the acid, or base, plays a part are determined by the magnitude of this constant. The researches on the decomposition of acetamide, and of methylic acetate, by water in presence of acids, have shewn that changes wherein 'predisposing affinity' and 'catalytic actions' are factors, are conditioned by the affinityconstants of the acids, as determined by the application of Guldberg and Waage's theory. And the researches on the action of acids on insoluble salts (see ante, par. 220) have shewn that the influence exerted by the stability of such salts on the equilibrium of the system is of the same kind as that exerted by the affinities of the reacting substances. Some of Ostwald's pupils have recently shewn that the solvent actions of various dilute acids on cream of tartar, and on the sulphates |