PRESIDENTIAL ADDEESS — SECTION B. 89 



solid state, leaving the other substance in solution. Thus 

 water freezes below 0°C., or ice melts below 0° when it is in 

 presence of dissolved salt ; but it is pure ice that separates. 

 Now, it has been deduced from theory as well as proved ex- 

 perimentally (by Eamsay and Young) that the freezing-point 

 of a liquid is that point — the only one — at which the curves 

 meet which represent the change of vapour-pressure of the 

 solid and of the liquid with change of temperature ; and the 

 forms of these curves are such that this common point must 

 necessarily fall at a lower temperature if by any cause the 

 vapour-pressure of the liquid is reduced. But we know that 

 the presence of dissolved matter does reduce the vapour-pres- 

 sure of a liquid, so that we have at once an explanation of the 

 lowering of the freezing-point in such cases. Moreover, for 

 very dilute solutions in one and the same solvent (but not other- 

 wise), it can be easily shown that this reduction of the freezing- 

 point is directly proportional to the reduction of vapour-pres- 

 sure, and so, as we have seen, to the osmotic pressure and to 

 the molecular concentration. 



Moreover, starting from the laws of osmotic pressure 

 and thermo- dynamical considerations, van't Hoff has shown 

 that the effect on the freezing-point can be calculated from 

 the absolute temperature of the original freezing-point of 

 the solvent and its latent heat of fusion^ and the numbers 

 calculated by him agree with the experimental numbers of 

 Raoult. The freezing-point of water is lowered 1-028° by the 

 solution of a substance in the ratio of one molecule to a 

 a hundred ; while in the case of acetic acid and of benzene the 

 effect is somewhat less — namely, 0'64°. Here, then, we have 

 another practical method for the determination of molecular 

 weights of substances to which the older methods cannot be 

 applied ; and, indeed, this is so simple and (with certain limita- 

 tions) so reliable that it might often be substituted for the 

 vapour-density method as a matter of choice. The apparatus 

 is of the simplest kind, provided a sufficiently delicate ther- 

 mometer be available. Obviously solvents are to be preferred 

 which, like the three I have named, have freezing-points not 

 far removed from the ordinary temperature of a laboratory, but 

 in special cases solvents of much higher or lower freezing-points 

 may be employed. 



To give an account of the interesting results that have been 

 obtained already by Raoult and the experimenters who have 

 followed him with this and the vapour-pressure methods as 

 applied to organic compounds would take too long ; but I may 

 direct your attention to the attempts to determine the mole- 

 cular weights of the metals by their effect on tire vapour-pres- 

 sure of mercury (Ramsay), on the freezing-point of sodium 

 (Tamman), and more particularly on the freezing-point of tin 



