﻿644 Prof. Porter and Mr. Hedges on the Law of 



being dy (reckoned positive when downwards). The concen- 

 tration of the solution at any depth is c where c = nm, m 

 the mass of a particle and n the number of particles per c.c. 

 (i. e., the numerical concentration). Considering the osmotic 

 pressure P, i. e. p—p , as being a function both of the hydro- 

 static pressure of the solution, p, and of the numerical 

 concentration, we have the mathematical identity 



^P_/?3P\ /3P\ dn dy 

 dp ~ Xdp ) n \dn) p 'dy'dp m 



oV u — s 

 Now 3- = , where 5 is the shrinkage*, and simple 



v A 1 S P ^ r • d ? 1 d Po u-o- 1 

 hydrostatic considerations give —5- =1 7— = ; also 



dp = g d P d 'P u 



dy a' 



^i c s — a a ^P dn 

 lnererore ==—.- — .-=-.. 



u g on ay 



This formula is exact, and is independent of any particular 

 hypothesis of the mechanism of the variation. 



Now it was shown by Sackur and by one of us that the 

 variation of P with concentration in the case of a sugar 

 solution can be represented very nearly, up to high concen- 

 trations, by the formula 



p_ nrT 



(l-bny 



where b is a constant which is of the same order of size as,, 

 but is larger than, a molecule of sugar. If we assume the 

 applicability of the same type of formula to a suspension of 

 gamboge 



n ~~ (l-bnf 



In these formulae r, which applies to an actual particle, is- 

 connected with the usual molecular gas constant, P (which 

 refers to one gram-molecule), by the equation 



r= <^- , where N is Avogadro's number. 



Hence -j- = .%-j^(l—bn) 2 . 



ay ua ±i l 



* Porter, Proc. Boy. Soc, A. 1907, p. 522. 



