We gain, only to see that more gain is possible; the opportunity for advance is infinite. Forever and ever thought can reach out into the unknown, and never need to weep because there are no more worlds to conquer. It was the study of electro-chemical changes which led Berzelius to his electro-chemical theory of combination, and then to the dualistic theory, which has already been mentioned. In or about the year 1832, when the Berzelian doctrines were at the summit of their fame, Faraday showed that the chemical power of a current was directly proportioned to the quantity of electricity which passed, and this led him to believe that chemical affinity and electric energy were identical. Electrolysis, the electrical decomposition of compounds in solution, was a special object of his attention, and by quantitative methods he found that the changes produced could be stated in terms of chemical equivalents or combining numbers. One equivalent weight of zinc consumed in the galvanic battery yields a current which will deposit one equivalent of silver from its solution, or which, decomposing water, will liberate one equivalent each of oxygen and hydrogen. All electro-chemical changes followed this simple law, which gave new emphasis to the atomic theory, and furnished a new means for measuring the combining numbers. In the early days of electro-chemistry the products of electrolysis were studied in the light of the dualistic theory. But as chemical investigation along other lines overthrew this hypothesis, a closer examination of electrolytic reactions became necessary. Electrical decompositions were dualistic in character, but the dualism was not that taught by Berzelius. When a salt, dissolved in water, is decomposed by the current it is separated into two parts, which Faraday called its _ions_; in Berzelian terms these were in most cases oxides, but this conclusion fitted only a part of the facts, and finally was abandoned. Whatever the _ions_ might be, they were not ordinary oxides. Many and long were the investigations bearing upon this subject before a satisfactory settlement was reached. The phenomena observed in solutions, raised still another question, that of the nature of solution itself, and this is not yet fully answered. Two lines of study, however, have converged, within recent years, to some remarkable conclusions, the latest large development of chemical theory. It has long been known that solutions of salts do not freeze so easily as pure water, and also that their boiling points are higher. In 1883 Raoult discovered a remarkable relation between the freezing point of a solution and the molecular weight of the substance dissolved, a relation which has since been elaborately studied by many investigators. From either the freezing-point depression or the elevation of the boiling point the molecular weight of a soluble compound can now be calculated, and many uncertain molecular weights have thus been determined.