_Molecular Weight Determinations._—Gas and vapor densities in connection with Avogadro’s principle, formed the only basis for molecular weight determinations until comparatively recent times. The early methods of Gay-Lussac and Dumas for vapor density were supplemented in 1868 by the method of Hofmann, whereby vapors were measured under diminished pressure over mercury. In 1878 Victor Meyer introduced a simpler method depending upon the displacement of air or other gas by the vapor in a heated tube. As refractory tubes, such as those of porcelain or even iridium, could be used in this method, molecular weights at extremely high temperatures were determined with interesting results. For instance, it was found that iodine vapor, which shows the molecule I_{2} at lower temperatures, gradually becomes monatomic with rise in temperature, that sulphur vapor dissociates from S_{8} to S_{2} under similar conditions, and that most of the metals, including silver, have monatomic vapors. In 1883 and later it was pointed out by Raoult that the molecular weights of substances could be found from the freezing points of their solutions, but this method was complicated from the fact that salts, strong acids and strong bases behaved quite differently from other substances in this respect, and allowances had to be made for the types of substances used. The complication was afterwards explained by the ionization theory of Arrhenius. Better apparatus for this method was soon devised by Beckmann, who introduced also a method depending upon the boiling points of solutions, and these two methods are still the standard ones for determining molecular weights in solution. They are very extensively employed by organic chemists. It has been found that the majority of substances when dissolved have the same molecular weight as in the gaseous condition, provided that they can be volatilized at comparable temperatures. For instance, sulphur in solution has the formula S_{8}, iodine is I_{2} and the metals are monatomic. _Van’t Hoff’s Law and Arrhenius’s Theory of Ions._—Modern views on solutions date largely from 1886, when van’t Hoff called attention to the relations existing between the osmotic pressure exerted by dissolved substances and gas pressure. Pfeffer, a botanist, was the first to measure osmotic pressure (1877). Basing his conclusions chiefly upon Pfeffer’s determinations, van’t Hoff formulated a new and highly important law, which may be stated as follows: The osmotic pressure exerted by a substance in solution is equal to the gas pressure that the substance would exert if it were a gas at the same temperature and the same volume. Further investigations have fully established the fact that molecules in dilute solution obey the simple laws of gases. It was pointed out by van’t Hoff that salts, strong acids and strong bases showed marked exceptions to his law in exerting much greater osmotic pressures than those calculated for them.