_ = ( 5l ^^)/™_ (8, 



602 The Earl o£ Berkeley and Dr. C. V. Burton on 

 By substituting in (3) we get 



-y^ = \ u — w — u-^ — ) /uw-^ — . . . (7) 

 dG: \ dp // £c 2 v ' 



Now, in Appendix I. (equation 29), it is proved that 



BPi _ u — s l 



~dp u ' 

 substituting in (7) we get 



Prof. Callendar, using a different notation, states* that 



s 1 — w=—Ctf}ivrdc 2 (9) 



(this relation can be easily proved), hence (8) becomes 



dti ~ utv'dFj/'dc, •••■■•■--_• ^ 1U ' 



Now consider the stratification in relation to P 2 , c 1? y, 

 and s 2 ; that is, the relations subsisting between the solution 

 and the pure solute in column EF. 



An equation exactly analogous to (10) will result, where 

 P 2 will replace P : when the solution at hydrostatic pressure p 

 is in osmotic equilibrium with the solute at pressure p — P 2 

 and Ci will replace c 2 ; the equation is 



da _ CicWcki m x 



d(Jr yw'd? 2 /dc 1 •••••• W 



Sipce . c 1 =l — c 2 we get 



dc 2 __ dc\ ~&w _ ~dw , "$V 1 _ BPi 



dGr~ dG' ~d?2~ 3^i ' ' Bci ~ ~^c 2 } 

 and also from (10) and (11) 



dPi/dc 2 _ __ c 2 y 



• Transformation^ 



The relations (8), (10), (11), and (12), have been obtained 

 from a simple consideration of equilibrium conditions ; but, 

 though »these equations are rigorously true, a difficulty 

 sometimes arises in their exact interpretation. For u, y are 



.* Iroc. Roy. £oc. Series -A, vol. lxxx. p. 470. 



(12) 



