The applicability of the law of Dulong and Petit to the determination of atomic weights has been frequently exemplified during the last sixty years; and a number of these constants have been rectified by its means—_e.g._, of thallium, uranium, glucinum, indium, etc. The anomalies presented by the cases of elements of low atomic weight—_e.g._, carbon, boron, silicon—have been further inquired into; and it has been shown by Weber, and independently by Dewar, that in the case of these substances the specific heat rapidly increases with the temperature, and approximates at high temperatures to a value required by the law of Dulong and Petit. Within recent years other methods of ascertaining molecular weights have been put at the disposal of chemists. These methods are especially valuable in the case of bodies which cannot be volatilised. They depend upon the influence of the substance (1) upon the freezing-point and (2) upon the boiling-point of a solvent. It has long been known that a substance in solution affects the freezing-point of the solvent, and in the great majority of cases depresses it. Sir Charles Blagden, as far back as 1788, showed that in aqueous solutions of inorganic salts the depression was proportional to the amount dissolved. It was subsequently found by Coppet that, in a number of solutions of similar salts where these were present in the ratio of their molecular weights, the solutions froze at practically the same temperature: the molecular depressions of the freezing-points differ from group to group but are nearly equal in groups of similar compounds. Raoult further observed that, when certain quantities of the same substance are successively dissolved in a solvent on which it exerts no chemical action, there is a progressive lowering of the point of solidification of the solution, and this depression is proportional to the weight of the substance dissolved in a constant weight of the solvent. In the case of a large number of solvents the depressions of the freezing-point, calculated for amounts proportional to the molecular weights of the dissolved substance, were nearly constant. Raoult pointed out that these relations between the molecular weights and the lowering in the freezing-point may be employed to determine the molecular weight of a soluble substance. The molecular weight _m_ is found from the expression _m_ = K/A, where A is the quotient obtained by dividing the observed depression in the freezing-point of the solvent by the percentage content of the solution, and K (the molecular depression) is a constant dependent on the solvent. Thus in the case of phosphorous oxide it was found that 0.6760 gram added to 20.698 grams of benzene—in which the oxide is soluble without change—lowered the freezing-point of the 3.16 per cent. benzene solution by 0°.68. Since the value of K for benzene is 49, we have (3.16 × 49)/0.68 = 227, which serves to indicate that P4O6 is the true molecular formula for phosphorous oxide. This