A method for determining the molecular weights of substances by the rise of boiling-point of their solutions was also devised by Beckmann, and it is frequently used. The process is analogous to that in which the depression of freezing-point is made use of. Every pure substance has a perfectly definite boiling-point, provided that pressure is constant; but if any substance is dissolved in a pure liquid, the boiling-point of the latter is raised; and it is found that the rise of boiling-point is proportional to the number of molecules of the dissolved substance present. As an example, let us calculate the molecular weight of iodine dissolved in ether from the rise in the boiling-point of the ether. The rise caused by the hundredth part of the molecular weight of a substance taken in grams, and dissolved in 100 grams of ether, is 0.2105°. Now, Beckmann found that 1,513 grams of iodine dissolved in 100 grams of ether raised the boiling-point of the ether by o. 126°. And to raise the boiling-point by 0.2105°, 2.53 grams of iodine would have been necessary; 2.53 is therefore the hundredth part of the molecular weight of iodine. It is possible to weigh iodine in the state of gas, for it is an easily volatilised element; and its vapour has been found to be 126 times as heavy as hydrogen. We have seen that this statement implies that a molecule of iodine gas is 126 times as heavy as a molecule of hydrogen gas ; and as a molecule of hydrogen consists of two atoms, a molecule of iodine gas is 252 times as heavy as an atom of hydrogen, or its molecular weight is 252. The number obtained from the density of the gas is accordingly almost identical with that obtained from the rise in the boiling-point of ether.

We have now studied four methods by means of which the molecular weights of elements and compounds have been ascertained ; they are :

(1) By determining the density of the substance in the state of gas with reference to hydrogen, and doubling the number obtained; for molecular weights are referred to the weight of an atom of hydrogen, while a molecule, it is believed, consists of two atoms.

(2) By measuring the osmotic pressure exerted by a solution of the substance, and comparing the pressure with that exerted by an equal number of molecules of hydrogen, occupying the same volume, at the same temperature.

(3) By comparing the depression in freezing-point of a solvent containing the substance in solution, with the depression produced by the hundredth part of the molecular weight in grams of a substance of which the molecular weight is known, and by then making use of the known fact that equal numbers of molecules produce equal depression in the freezing-point of a solvent.

(4) By a similar method applied to the rise in boiling-point of a solvent caused by the presence of a known weight of the substance of which the molecular weight is required.