270 The Earl of Berkeley,: Notes 



Now change the upper limits in (3) and (4) to p' =p + dp 

 -and -v|r , = ty + tfy, and we get 



. p + dp /*\p p + d\P 



s & dp = a dp 



and 



(-td+dp r»\p p +diP 



s b dp= I (Tpdp, 



from which it is easy to see that 



s b 0p 



(6) 



This result is of theoretical interest, and may have a 

 practical bearing on future experimental work. 



A possible Connexion between the Characteristic Equations 

 of Gases and of Solutions. 



In a paper entitled " Solubility and Supersolubility from 

 an Osmotic Standpoint " (Phil. Mag. 1912, vol. xxiv. p. 254), 

 which will be referred to as " S and S " throughout this com- 

 munication, it was shown that when either of the two 

 osmotic pressures of a binary liquid mixture is expressed as a 

 function of the concentration, these functions each contain 

 a logarithm which, in the limit, becomes infinite. 



Unfortunately, the proof of this proposition was but very 

 briefly outlined, and, as the matter is of some importance 

 for osmotic theory, it seems advisable to give a more detailed 

 exposition. 



In " Contribution to the Osmotic Theory of Solutions " * 

 (which will hereafter be referred to as " Theory ") it is shown 

 that (using a different notation) SFJSp — ^^—sjjz^. 



As the value of sjz & is, in the majority of cases, close to 

 unity, it is easy to see that the change in P a is but a small 

 fraction of the change in p, so that although a change in the 

 concentration leads to a change both in p and P , the con- 

 tribution due to the former is but small. 



* Berkeley & Burton, Phil. Mag. vol. xvii. 1909, p. 604. 

 In this paper there are numerous errata ; the more important are given 

 ".below. 



Page 604, equation (17), the sign governing the right-hand member 

 should be positive. 

 „ 606, it should have been explained that the concentrations are 



differently expressed in Margule's equation. 

 „ 611, lines 8 and 9 from bottom, cjzv should be iv/c^ 

 } , 612, the expressions in lines 8 and 10 from bottom should be 

 multiplied by a factor dcjdh. 



