x / ( n - x ) , until with an infinitely large quantity m the fraction x / n will equal 1, and the decomposition will be complete, however small the affinities uniting MY and NX may be; and (3) if m = n , by taking MX + NY or MY + NX we arrive at one and the same system in either case : ( n - x )MX + ( n - x )NY + x MY + x NX. These direct consequences of Berthollet's teaching are verified by experience. Thus, for example, a mixture of solutions of sodium nitrate and potassium chloride in all cases has entirely the same properties as a mixture of solutions of potassium nitrate and sodium chloride, of course on condition that the mixed solutions are of identical elementary composition. But this identity of properties might either proceed from one system of salts passing entirely into the other (Bergmann's hypothesis) in conformity with the predominating affinities (for instance, from KCl + NaNO 3 there might arise KNO 3 + NaCl, if it be admitted that the affinities of the elements as combined in the latter system are greater than in the former); or, on the other hand, it might be because both systems by the interchange of a portion of their elements give one and the same state of equilibrium, as according to Berthollet's teaching. Experiment proves the latter hypothesis to be the true one. But before citing the most historically important experiments verifying Berthollet's doctrine, we must stop to consider the conception of the mass of the reacting substances. Berthollet understood by mass the actual relative quantity of a substance; but now it is impossible to understand this term otherwise than as the number of molecules, for they act as chemical units, and in the special case of double saline decompositions it is better to take it as the number of equivalents. Thus in the reaction NaCl + H 2 SO 4 the salt is taken in one equivalent and the acid in two. If 2NaCl + H 2 SO 4 act, then the number of equivalents are equal, and so on. The influence of mass on the amount of decomposition x / n forms the root of Berthollet's doctrine, and therefore we will first of all turn our attention to the establishment of this principle in relation to the double decomposition of salts.
About 1840 H. Rose29 showed that water decomposes metallic sulphides like calcium sulphide, CaS, forming hydrogen sulphide, H2S, notwithstanding the fact that the affinity of hydrogen sulphide, as an acid, for lime, CaH2O2, as a base, causes them to react on each other, forming calcium sulphide and water, CaS + 2H2O. Furthermore, Rose showed that the greater the amount of water acting on the calcium sulphide, the more complete is the decomposition. The results of this reaction are evident from the fact that the hydrogen sulphide formed may be expelled from the solution by heating, and that the resulting lime is sparingly soluble in water. Rose clearly saw from this that such feeble agents, in a chemical sense, as carbonic anhydride and water, by acting in a mass and for long periods of time in nature on the durable rocks, which resist the action of the most powerful acids, are able to bring about chemical change—to extract, for example, from rocks the bases, lime, soda, potash. The influence of the mass of water on antimonious chloride, bismuth nitrate, &c., is essentially of the same character. These substances give up to the water a quantity of acid which is greater in proportion as the mass of the water acting on them is greater.30
Barium sulphate, BaSO 4 , which is insoluble in water, when fused with sodium carbonate, Na 2 CO 3 , gives, but not completely, barium carbonate, BaCO 3 , (also insoluble), and sodium sulphate, Na 2 SO 4 . If a solution