288 Mr Vegard, On some general Properties 



Equation (30) then takes the form 



{mo)" mo 



• jr in 



V'dp 



Pr Jo 



Mr g/ 



mr TT^ dm... 

 omr 



In general we have 



^= ,„.. \ ■ -0,1. 2... (.-1). 

 V dp I 7n^ ;r^ dm^ 



Pr J omr 



Taking the sum of these equations from i = to i=r — 1, 



r—l r—1 



^(mi)" S mi 







I V'dp mrr^dnir 



Jpr h (^l^r 



IF. 



but — = .^-, — r77 = specific volume of a solution of .concentrations 

 p Z{mi) _ ^ 



Ci, Ca ... c,._i , and introducing 



mo + mi + ... mr-i 

 the osmotic pressure will be defined by the equation 



(31a) [''-, dp = p/f, 1^ dKr. 



1 . 1 . . 



If — > is the mean value of - in the interval P — »,. we get for 



pm p 



the osmotic pressure Q,. 



(316) Qr = pjf^jKr^^dKr. 



This expression is well known for binary solutions, and we see 

 that with a proper modification of the quantities p^, Kr and f^ 

 the same expression holds for the partial osmotic pressure. 



§ 8. Osmotic pressure of the first order. 



When the secondary solution only contains one substance, we 

 shall designate the corresponding osmotic pressure to be of the 

 first order. Let tti denote the osmotic pressure, when the mem- 

 brane is permeable to the substance (^). From the (condition of 

 equilibrium we get in the usual way 



(32) -p= ^dp=gi-U 



Pmi J Pi Pi 



