the Osmotic Theory of Solutions. 617 



This result Is obtained by Prof. Porter by differentiating 

 equation (1) o£ his first paper ; but by the method followed 

 the relation is obtained as an exact equation whatever 

 .assumption is made as to the volatility of solute and solvent. 



Appendix 2. 



In his recent paper on vapour-pressure and osmotic pres- 

 sure, Prof. Callendar * has discussed the differences of 

 concentration to be found in a column of cane-sugar solution 

 (at 0° C), which has attained a state of final equilibrium 

 under gravity as shown in fig. 1 by column AB (we must 

 here assume that B is a semi-permeable membrane in contact 

 with the free surface of water, and that the vapour-pressure 

 of the solution at A is in equilibrium with that of the water 

 at the same level). Prof. ( Jallendar assumes that the con- 

 centration and osmotic pressure at A is given by Berkeley 

 and Hartley's results f, and calculates the concentration just 

 above B by means of the approximate relation 



dc 2 /c 2 — — P (dw/dP 2 )/w, . 



(30) 



in which P is the mean osmotic pressure in the column. 



In revising these estimates, we have taken the concen- 

 tration and osmotic pressure just above B as given by the 

 experiments (this is more correct than Prof. Callendar's 

 (procedure in that the conditions in the experiments only 

 differ from those indicated above by the fact that there is a 

 pressure on the water of one atmosphere instead of that of 

 its vapour only), and have calculated the concentration at 

 the top of the column at A, by using a relation which, in the 

 first instance, can be written down exactly, and allows our 

 calculation to be carried to any degree of precision for which 

 the accuracy of the data suffices. 



In (2(j), put F = 0, since we are dealing with equilibrium 

 •conditions ; then remembering that dp = <jdlijw, we get the 

 exact relation 



dp = s 1 /(s 1 — w) . fcPj/tocj . dc 2 . 



(31) 



Neglecting the density of the vapour in comparison 

 with that of the solution, and the pressure of the vapour in 



* Proc. Roy. Soc, Series A, vol. lxxx. p. 473. 

 t Phil. Trans., Series A, vol. ccvi. p. 503. 



