Permeability 7 
as a gas occupying the volume of the solvent only and not the volume 
of the solution. Even so, the divergence is not eliminated, and con¬ 
sequently various formulae have been put forward to relate more 
exactly the concentration, temperature and osmotic pressure of 
solutions. A consideration of these is outside the scope of this work, 
and the reader is referred to the authorities already cited. It may, 
however, be emphasized that the simple van’t Hoff law is valid 
for dilute solutions. 
It has been pointed out that the deviations of concentrated 
solutions of sucrose from the behaviour of “ideal” solutions may to 
a large extent be explained on the assumption that sucrose is hydrated 
in solution, that is, that with each molecule of sugar a certain number 
of molecules of water become associated. In concentrated solutions 
this may materially reduce the quantity of solvent and so increase 
the concentration of solute, and consequently the osmotic pressure, 
in the way actually observed. In dilute solutions, where the quantity 
of solvent is very large in proportion to the quantity of solute the 
influence on concentration of solute is negligible (Nernst, 1911; 
Findlay, 1913). 
Measured Values of the Osmotic Pressure of Sucrose. 
A consideration of the work of Berkeley and Morse and their 
respective collaborators is sufficient to indicate the very great care 
and persistence required for the exact determination of osmotic 
pressures. Fortunately the substance most carefully studied, namely, 
sucrose, is one of particular importance for the student of per¬ 
meability in plants, as will appear in a later chapter. It will therefore 
be useful to record here a few of the values obtained by Morse and 
regarded by him as established with a reasonable degree of certainty. 
In the following table are therefore given the values for the osmotic 
pressure of sucrose in different concentrations at temperatures most 
generally encountered in working with plants. For values at other 
temperatures, as well as for values of the osmotic pressure of solu¬ 
tions of glucose and mannite reference must be made to the summary 
of his work made by Morse (1914). 
