other, is as old as philosophy, 'was first applied to its explanation by the English chemist Dalton in 1807. He suggested that the ultimate particles of matter, or atoms between which union is assumed to take place, have a definite weight; in other words, that they are distinct masses of matter. In the combination of the two elements in question, therefore, an atom of iron unites with an atom of sulphur to form a molecule of sulphide of iron; and the union takes place in the proportion by weight of fifty-six to thirty-two, simply because these numbers represent the relative weights of the two sorts of atoms. Now, Dalton may be wrong, and there may be no such things as atoms; but every science postulates fundamental principles, of which the only proof that can be offered is a certain harmony with observed facts; and the chemist assumes the reality of atoms and molecules because they enable him to explain what would otherwise be a chaos of unrelated facts. The combining proportions of substances, then, indicate their relative molecular weights; and, bearing this in mind, we must turn again for a moment to the physical side of the question, to inquire whether, and in what way, the physicist can determine the weight of a molecule.
Water, alcohol, and ether expand when heated, like other forms of matter, but they do so very unequally. Their vapors, on the other hand, are expanded by heat at exactly the same rate under like conditions. The theory supposes that the molecules which are close together in the liquids become widely separated when these are converted into vapors; and the action of the particles on each other becomes less and less as they are driven farther apart by heat, until at last it is inappreciated. When the molecules of the vapors in question are thus freed from other influences, it is found that heat acts in an exactly similar manner upon each of them; and this is found to be true of all gaseous bodies. The obvious explanation in the case before us is, that there are the same number of particles within a given space in the vapors of all three liquids. This is the law of Avogadro, which is formulated as follows: "Equal volumes of all substances, when in the form of gas, contain the same number of molecules"; and we shall see how simply this conception is applied for the purpose of determining the molecular weights of all bodies which are capable of being vaporized. It will be understood that we are still dealing, as in the case of chemical combination, with relative weights only. We have no means of ascertaining the absolute weight of a molecule of any substance; but we can state with perfect accuracy what relation these weights bear to one another. For this purpose, the molecule of hydrogen, which is the lightest body known to science, has been selected as the unit. Calling the weight of a litre of hydrogen one, we find by the balance that a litre of oxygen weighs sixteen; and as, by Avogadro's law, both litres contain the same number of molecules, the molecule of oxygen is sixteen times heavier than that of hydrogen. The mo-
