80 



OSMOTIC PRESSURE OF AQUEOUS SOLUTIONS. 



time. The validity of the proof depends, however, upon the question 

 whether the pressures obtained by Pfeffer were the full (maximum) 

 pressures of his solutions. Pfeffer believed them to be so; for he men- 

 tions having ascertained, by means of specific-gravity determinations, 

 that the solutions did not lose appreciably in concentration while in the 

 cells. It is questionable, however, if this method is sufficiently delicate, 

 unless carried out with extraordinary precautions, to detect differences 

 which, if discovered, might well have led to a verdict unfavorable to the 

 applicability of Boyle's law. The writer and his associates have not 

 yet exactly repeated the experiments of Pfeffer, though they expect to 

 do so in the near future. They have, however, done enough work at 

 temperatures and concentrations approximating to those of Pfeffer to 

 enable them to predict with considerable confidence about what the 

 pressures in question will be found to be. The following table gives 

 the pressures found by Pfeffer which have been universally quoted as 

 proof of the conformity of osmotic pressure to Boyle's law and those 

 which the work of the writer and his associates enable them to predict : 



Table 3. 



If we compare the pressures found by Pfeffer with those required by 

 the law of Boyle at 15° — that is, columns 2 and 3 — the agreement is 

 astonishing, and it is not surprising that these data have played an 

 important part in nearly all discussions of osmotic pressure during the 

 last twenty-five years. If, on the other hand, we compare the pres- 

 sures of Pfeffer with those calculated for the same solutions from the 

 results of the author and his associates — that is, columns 2 and 4 — it 

 will be observed that the latter are considerably higher than the former. 

 The differences (column 5) vary from 5.6 to 10.4 per cent. The data 

 given in column 4, which are designated (somewhat presumptuously 

 perhaps) as "the pressures which Pfeffer should have found," are all 

 calculated from measurements made after the method of measuring had 

 been brought to its highest state of perfection — that is, after the last 

 vestige of leakage of solute had been eliminated. The inference to be 

 drawn from the facts, as stated above, is that the smaller pressures of 

 Pfeffer were due to some leakage of the solute. The solutions of Pfeffer 

 which are cited in this discussion contained in 1,000 cubic meters of 



