Supersolubility from the Osmotic Standpoint, 261 



from which 



(5) 



^Pi c 2 u 2 dP 2 



Now the conjugate osmotic pressure-curve starts from D as 

 a straight line (Boyle's law), hence ~d IVBol = a constant = & ; 



On integrating this expression and remembering that c x is 

 vanishingly small, it follows that P T must at the limit contain 

 an infinite logarithm and must therefore be infinite. 



The conjugate osmotic pressure-curve is essentially similar, 

 and cuts the ordinate through C at some point which we 

 cannot specify _, say at G, it then leaves BE at H, where 

 BH = CG. and approaches the ordinate through A 

 asymptotically. 



(13) If we take some other constant temperature we shall 

 obtain another pair of curves in which the position of the 

 points E, F, G, and H will be different. Similarly if we 

 take some other constant pressure on the solutions. And, in 

 general, given the pressure (or temperature), E and F will 

 coincide at a definite temperature (or pressure) (G and H 

 will coincide simultaneously on the same ordinate), this 

 point being the critical osmotic pressure and concentration 

 for the particular pressure (or temperature) concerned ; 

 that is, the point where the two liquids become miscible in 

 all proportions. The locus of the points E and F will 

 be the u border curve " for the ordinary osmotic pressure, 

 while the locus of G and H is the border curve for the 

 conjugate. 



(14) If we were to plot the curves for osmotic pressures 

 defined by the condition that the pressure on the solvent and 

 the solute respectively were constant, in general, the principal 

 modification would be that, for the conjugate, neither of 

 the points of limited solubility would be on the same ordinates 

 as those of the ordinary osmotic pressure. 



(15) We will now discuss the inferences which may be 

 drawn from the curves. 



Dealing first with the paths between E and F, and G and 

 H ; all experience with single-phase systems shows that their 

 properties are throughout continuous — we may therefore 

 safely postulate that E and F (and G and H) must be joined 

 in a smooth manner — and, as BE = CF, the only way to do 

 this is to carry on the curve AE upwards and MF downwards, 

 and join them by a curve containing at least two points where 

 BFi/^^2 = 0? sa y a ^ K and L. From equation (5), when 



