Experimentally this important fact was proved first by Berzelius, who showed that by oxidizing lead sulphide, PbS, to lead sulphate, PbSO4, no excess either of sulphur or lead could be found after oxidation; the same held good with barium sulphite, BaSO3, when converted into barium sulphate, BaSO4. On a much larger scale and with very great accuracy the inverse was proved half a century later by J.S. Stas, who reduced silver chlorate, AgClO3, silver bromate, AgBrO3, and silver iodate, AgIO3, to the corresponding binary compounds, AgCl, AgBr and AgI, and searched in the residue of the reaction for any excess of silver or halogen. As the tests for these substances are among the most sensitive in analytical chemistry, the general law underwent a very severe test indeed. But the result was the same as was found by Berzelius--no excess of one of the elements could be discovered. We may infer, therefore, generally that compounds enter ulterior combinations without change of the ratio of their elements, or that the ratio between different elements in their compounds is the same in binary and ternary (or still more complicated) combinations. This law involves the existence of general combining weights just in the same way as the law of neutrality with double decomposition of salts involves the law of the combining weights of acids and bases. For if the ratio between A and B is determined, this same ratio must obtain in all ternary and more complicated compounds, containing the same elements. The same is true for any other elements, C, D, E, F, &c., as related to A. But by applying the general law to the ternary compound ABC the same conclusion may be drawn as to the ratio A : C in all compounds containing A and C, or B : C in the corresponding compounds. By reasoning further in the same way, we come to the conclusion that only such compounds are possible which contain elements according to certain ratio-numbers, i.e. their combining weight. Any other ratio would violate the law of the integral reaction of compounds. As to the law of multiple proportions, it may be deduced by a similar reasoning by considering the possible combinations between a compound, e.g. AB, and one of its elements, say B. AB and B can combine only according to their combining weights, and therefore the quantity of B combining with AB is equal to the quantity of AB which has combined with A to form AB. The new combination is therefore to be expressed by AB2. By extending this reasoning in the same way, we get the general conclusion that any compounds must be composed according to the formula A_m B_n C_p..., where m, n, p, &c., are integers.