274 The Earl of Berkeley : Notes 



"Theory" (note that the a a is supposed to be measured 

 under the total pressure of the mixed vapours or gases). 



In a similar manner the whole of the cycle on pages 609 

 to 812 of "Theory" can be carried out for a column of mixed 

 vapours (or gases) ; hence equations {26) and (31), pages 612 

 and 617, need only be translated into terms denoting the 

 physical properties under discussion for them to be ap- 

 plicable. 



Thus (31) is 



d/3 «■„-». V (10) 



This equation mast be satisfied in the solution of the 

 problem of the stratification of two vapours or gases by 

 gravity. This relative concentration is ordinarily evaluated * 

 by assuming that Boyle's and Dalton's laws hold for the two 

 components in the mixture; but equation (10) is exact, and 

 independent of this assumption. 



It may be verified that 



holds for mixed vapours. This equation is the analogue 

 ■of (18), p. 604 "Theory." If we combine (11) with (18) of 

 "Theory " and remember that sjs b — ajcr^ we get 



* d£ ' d* a lb i da ' 



Conditions to be fulfilled by an Equation of State for Osmotics. 



We can now state some of the conditions that appear to 

 be required in the osmotic equation of state ; thus expressing 

 P a as a function of b, we have the following : — 



(1) The graph of P a near the origin is nearly linear over 



a finite range. 



(2) The expression for P a must become infinite with 



log 1/6 as b approaches zero. 



(3) As shown in " S and S" p. 260, there must be two 



points where d~PJdb = 0. 



* Fundamentally in the ordinary method, H a is put equal to ir^ (the 

 partial pressure of the other component), and 7r« is also assumed to 

 equal Tc b , It would seem that this latter hypothesis could be tested 

 experimentally, and the experiments would be of considerable importance; 

 but probably the discovery of suitable membranes is necessary before 

 we can verify that n a = ^ . 



