1909] on Osmotic Phenomena. 487 



deduct the volume occupied by the sugar molecules themselves in 

 order to arrive at the space in which they were free to move. 

 Unfortunately the later and more accurate series of measurements by 

 the same experimentalists at 0°C. and S'' C, gave nearly the same 

 osmotic pressures as at 24° 0:, and would appear to show, either that 

 there is little or no increase of osmotic pressure with temperature, 

 and that the pressures at 0°C. are much greater than those given by 

 their extension of the gas-pressure analogy, or that one or other of 

 the series of experiments are in error. 



About the same time Lord Berkeley and E. J. Hartley undertook 

 a series of measurements of the osmotic pressures of solutions of 

 various kinds of sugar at 0°C. bya greatly improved experimental 

 method, which permitted the range of pressure to be extended to 

 upwards of 100 atmospheres. Instead of allowing the solvent to 

 diffuse into the solution until the equilibrium pressure was reached, 

 they appHed pressure to the solution until balance was attained. 

 The method of Lord Berkeley and Hartley possesses several obvious 

 advantages, and it is impossible to study the original memoir without 

 being convinced that they have really measured the actual equilibrium 

 pressures with an order of certainty not previously attained or even 

 approached. The pressures found were in all cases greatly in excess 

 of those calculated from the gas-pressure of the sugar molecules in 

 the volume occupied by the solution (according to van 't Hoff's 

 formula for dilute solutions), or even in the restricted volume 

 occupied by the solvent (according to Morse and Frazer's assumption). 



Lord Berkeley endeavoured to represent these deviations on the 

 gas-pressure analogy by employing a formula of the van der Waals 

 type, with three disposable constants. Out of some fifty formulae 

 tested, the two mftst successful were those given in Table L The 

 constants A, a, and h were calculated to fit the three highest observa- 

 tions for each solution. Values calculated by the formulae for the 

 lower points were then compared with the observations at these 

 points, with the results given in Table I. for cane-sugar. It is at 

 once evident that, even with three constants, the gas-pressure analogy 

 does not represent the results satisfactorily within the limits of error 

 of experiment. Moreover, with three constants the equation cannot 

 be interpreted, so that the gas-pressure analogy becomes useless as 

 a working hypothesis, or as a guide to further research. On the 

 vapour-pressure theory, to be next explained, the results are much 

 better represented, as shown in column C, with but a single constant, 

 and that a positive integer with a sunple physical meaning. 



Vapour-Pressure Theory. 



On the vapour-pressure theory, osmotic equilibrium depends on 

 equality of vapour-pressure and not on an imaginary pressure which 

 the particles of the dissolved substance would exert if they were in 



Vol. XIX. (No. 103) 2 k 



