All pure substances have a perfectly definite melting-point; thus, ice melts at o° C, sulphur at 1200, tin at 2260, lead at 325% and so on. These temperatures are also the freezing-points of the liquids, provided some of the solid substance is present. If this is not the case, then it is possible to cool the liquid below its freezing-point without its turning solid. Accordingly, water freezes at o° if there is a trace of ice present; melted tin solidifies at 226° if there is a trace of solid tin added to the cooled liquid; and if, for example, water be cooled without the presence of ice, until it has a temperature lower than o°, say 0.50 below o°, on addition of a spicule of ice a number of little crystals of ice begin to form in the liquid and the temperature rises to o°. But if there is some substance dissolved in the liquid, as, for example, sugar in the water or lead in the tin, then the freezing-point is lowered below that of the pure substance. And when the solvent freezes, in general the solid consists of the solid solvent, none of the dissolved substance crystallising out with it. It is owing to this fact that travellers in Arctic regions manage to get water to drink; for the ice from salt water is fresh, and when melted yields fresh water.

It has been observed that with the same solvent the freezing-point is lowered proportionally to the amount of dissolved substance present, provided the solution is a dilute one. Thus, a solution of cane-sugar in water, containing 3.42 grams of sugar in 100 grams of the solution, froze at o. 1850 below zero; and one containing half that quantity, 1.71 grams, froze at 0.0920 below zero. Again, the same lowering of the freezing-point is produced by quantities proportional to the molecular weights of the dissolved substances. Malic acid, an acid contained in sour apples, has the molecular weight 134, while it will be remembered that the molecular weight of cane-sugar is 342. Now, a solution of 1.34 grams of malic acid in water, made up with water so that the whole solution weighed 100 grams, froze at o. 1870 below zero, a number almost identical with that found for sugar.

Solvents other than water may also be used; but in that case the lowering of the freezing-point is different. Acetic acid, which is vinegar free from water, is often employed; so also is benzene, a compound separated from coal-tar, produced in the manufacture of coal-gas. The freezing-point of acetic acid is 170; that of benzene is 4.90. It was found in 1884 by Raoult, Professor of Chemistry in Grenoble in the South of France, that while 1.52 grams of camphor (the hundredth part of its molecular weight) dissolved in benzene (100 grams of solution) lowered the freezing-point of the benzene by 0.5140, the same quantity of camphor, forming a solution in acetic acid of the same strength, lowered the freezing-point of the latter by 0.39°. And he also noticed that the lowering of the freezing-point is proportional, at least in some cases, to the molecular weights of the solvents. Thus, the molecular weights of acetic acid and benzene are respectively 60 and 78; and as 0.39 : 0.514 : : 60 : 79, the proportionality is very nearly exact.

It is possible by this means to determine the molecular weight of any substance which will dissolve in any solvent for which the depression produced in the freezing-point is known. Thus, for example, Beckmann, the deviser of the apparatus with which such determinations are made, found that a solution of naphthalene, a white compound of carbon and hydrogen contained in coal-tar, in benzene, the solution containing 0.452 per cent, of naphthalene, lowered the freezing-point of benzene by 0.1400. A 1 per cent, solution would therefore cause a lowering of 0.3090. And as 0.309 : 0.39 :: 100 : 126, this is therefore the molecular weight of naphthalene. The simplest formula for naphthalene is C5H4, for its percentage composition is carbon, 93.75, hydrogen, 6.25; and to find the relative number of atoms, the percentage of carbon must be divided by the atomic weight of carbon, and that of hydrogen by its atomic weight, thus :93*75 7.81, and = 6.25 ; and these numbers are to each other in the proportion 5 : 4. But a substance with the formula C5H4 must have the molecular weight (5 x 12) 4- (4 x 1) = 64 ; whereas the molecular weight found is 126. Now, 126 is nearly twice 64; hence the formula of naphthalene must be C10H8. The method is not exact, but it affords evidence which, taken in conjunction with the analysis of the compound, enables the molecular weight to be determined.