136 Dr. Thomas Ewan on 



Ramsay and Young,* that for a gas or liquid at constant 

 volume the pressure may be represented by an equation of 

 the ioxmp = bT-a where b and a are constants. From this 



follows (,m) =&= constant. The same result follows from 



Van der Waals' equation. 



Equation 8 shows that the osmotic pressure' may decrease 



when the temperature rises, or (cmj may be negative. The 



bP 



sign of r™ is the same as that of k, which depends chiefly, 



as equation 4 shows, on the sign and magnitude of -—. k 



will be - when ~ is + , and the sum of the terms contain- 

 dw 



ing c and -y in equation 4 is greater than the term con- 

 taining w . 



(c) If we put from equation 8 

 bP^ 



Rk = v Y — J iii equation 7. 



it becomes 



from which 



'W?\ . ™/*Q 



Vv = Tv ^J + 



JM< 



diu 



/bP\ = P_JM ^Q 

 UtA~T Tv dw 



This last equation becomes, when -p = 0. 



VbTA~T 



That is at constant volume the osmotic pressure of a 

 solution is proportional to the absolute temperature when 

 the heat of dilution of the solution is zero. This result was 

 obtained by Van't Hoff. {Joe. cit p. 11). 



* Phil. Mag. (5) 23, 435, 1887. 



