OSMOTIC PRESSURE IN PLANTS 79 



neglected, and the equation can be thrown into the form 



Now, when n represents the number of gramme -mole- 



cules of solute, and N those of solvent, x = T . Accord- 



N + w 



ingly, for infinitely dilute solutions, n becomes negligible 

 in comparison with N, and x = ; thus, the fraction being 

 now very small, x 2 and higher powers may be neglected, 



T>rp 



the equation becoming P = . . But the water in the 



V JN 



solution occupies the volume NV , which for very dilute 

 solutions is practically the volume of the solution V. Thus 



T>np 



one arrives at the Van't Hoff equation P = -^". The 



latter is clearly a limiting case of the more general 

 form. 



When allowance is made for the association of water 

 and for the formation of a pentahydrate in aqueous sucrose 

 solutions, the values calculated by the equation for ideal 

 solutions agree well with the direct determinations of 

 Lord Berkeley and E. G. J. Hartley over a wide range of 

 concentrations. 



THE NATURE OF OSMOSIS. 



When a solution and the pure solvent are placed in direct 

 contact, diffusion proceeds till the concentration is uniform 

 throughout. But when a semi-permeable membrane is 

 interposed between them, such uniformity can never be 

 reached. By increase of pressure, however, the vapour 

 pressure of a solution may be raised so as to equal that of 

 the solvent. Thus when under sufficient pressure a solu- 

 tion may be in equilibrium with pure solvent. The inter- 



