18 SCIENCE PROGRESS. 



ing" gaseous pressure by osmotic pressure, gaseous laws 

 may be employed to express the behaviour of dissolved 

 substances when in dilute solutions. In this condition, 

 it has to be noted that dissolved substances so far re- 

 semble ceases that the actual volume of their molecules is 

 negligable as compared with the space which they inhabit, 

 that is, the volume of the solution, and further that their 

 energy is independent of the volume — there is no thermal 

 change in dilution. The validity of the application of 

 the gaseous laws to solutions can be tested by other 

 means than by observations on osmotic pressure. It can 

 be shown, apart from any theory as to the mechanism of 

 osmotic pressure, that solutions in the same solvent, 

 having the same osmotic pressure, must have the same 

 vapour pressure and boiling point and the same freezing 

 point. But according to the gaseous analogy, solutions 

 having equal osmotic pressures, or isotonic solutions as they 

 are called, must have the same molecular concentration ; 

 hence, according to the analogy, solutions having the same 

 freezing point and vapour pressure must contain per unit 

 volume the same number of dissolved molecules. More- 

 over, assuming the validity of Avogadro's hypothesis as 

 applied to solutions, van't Hoff has deduced thermody- 

 namically how the vapour pressure and freezing point of 

 these equimolecular solutions should vary from solvent to 

 solvent. Evidence as to the validity of the analogy can 

 thus be obtained from measurements on vapour pressure 

 and freezing point, measurements much more easily carried 

 out than the difficult observations on osmotic pressure. 



It is proposed in the present articles to summarise the 

 results of the main researches which have been made in 

 connection with the new theory of solutions, and in treat- 

 ing the subject-matter attention has been paid to the 

 exceptional behaviour of certain solutions. 



The laws which have been applied to dilute solutions 

 are to be regarded as limiting laws which would be 

 obeyed by an ideal solution. And just as certain gases 

 deviate from the ideal gaseous laws, some containing 

 fewer and others more molecules than Avogadro's 



