MEASUREMENT OF OSMOTIC PRESSURE 547 



obeyed the gas laws, the agreement afforded further proof of the 

 numerical agreement between the two sets of phenomena. 



It must now be admitted that the evidence on which van't 

 HofFs magnificent generalisation was based was of a very 

 inexact character. . Thus, whilst Pfeffer's observations showed a 

 general tendency for osmotic pressure to increase with rising 

 temperature, the individual figures pursued a zig-zag course, 

 departing (in a range in which the whole change of osmotic 

 pressure was only 10 per cent.) by as much as 3 per cent, 

 from the smoothed values calculated by van't Hoff. Again, 

 in using Raoult's " molecular depressions of the freezing-point " 

 as confirming his laws of osmotic pressure, van't Hoff's figures 

 showed deviations up to 6 per cent., whilst the values for 

 the " molecular lowering of vapour pressure " showed differences 

 up to 10 per cent, between the observed and the calculated 

 values. The situation presents, indeed, many similarities to 

 the circumstances under which Dalton promulgated his atomic 

 theory on the basis of data so inaccurate that he was able 

 to recognise the presence of a single equivalent of nitrogen 

 both in nitric oxide and in ammonia, two compounds in which 

 the actual proportions differ no less than 50 per cent. ! But 

 in each case the generalisation was so bold and far-reaching 

 that its inherent truthfulness was at once recognised, in spite of 

 the inexact character of the evidence which could be produced 

 in its support. In the case of the atomic theory, Berzelius 

 and Stas carried out series of exact measurements which 

 established beyond all question the validity of the atomic theory 

 as an accurate expression of the laws of chemical combination. 

 In the case of van't Hoff's generalisation, measurements of 

 similar exactitude, made by Griffiths at Cambridge, proved that 

 the formula could be applied accurately to calculate the de- 

 pression of the freezing-point of water by cane sugar and by 

 potassium chloride at extreme dilutions. But all the accurate 

 measurements of osmotic pressure that have since been made 

 have gone to prove that, whilst van't Hoff's law may give 

 an exact representation of the properties of very dilute solutions, 

 it fails utterly to express the properties of solutions of even 

 moderate concentrations and is of value mainly in providing 

 a base line for the study of the deviations which they exhibit 

 from the requirements of this law. 



The exact measurement of osmotic pressure is therefore 



