78 SOME RECENT RESEARCHES IN PLANT PHYSIOLOGY 



ture, K a constant almost identical with the gas equation 

 constant, and n is the number of gramme -molecules of 

 solute in the volume V of solution. But this he directly 

 states to be applicable only in the case of infinitely 

 dilute solutions, for in them the heat effect of further 

 dilution is negligible. Thus it is not surprising that the 

 equation was not found to hold good for concentrated 

 solutions, and though by Morse's substitution of the volume 

 of the pure solvent for that of the solution a better agree- 

 ment is obtained between observed and calculated values, 

 this is in reality due to its being an approximation to a 

 more recent equation expressly constructed for concen- 

 trated solutions. 



Owing to the formal identity of the gas laws and those 

 of dilute solutions, it was thought that a modification of 

 the equation might be capable of correctly representing 

 the behaviour of concentrated solutions, just as those of 

 the Van der Waal's type were found suitable for gases. 

 Two equations of this kind have been shown to give a fair 

 degree of agreement between calculated and observed 

 values of osmotic pressure over a moderately extended 

 range. 



The most generally applicable equation, however, is 

 that deduced thermodynamically for ideal solutions 

 namely, those composed of two unassociated liquids which 

 are completely miscible without occurrence of heat, volume, 

 or chemical changes. This general equation is : 







In this x is the ratio of the number of molecules of solute 

 to the total number of molecules present ; V is the molec- 

 ular volume of the solvent under the standard pressure; 

 whilst a represents the coefficient of compressibility of the 

 solvent. For moderate pressures the last factor may be 



