Theory of the Ideal Dilute Solution. 523 



which, since it holds to the first order of small quantities; inav 

 be written 



Pi—Pi — Tri — vri 



Pi' ITl' " 



Now equation [5] may be written 



IT 



so that for a dilute solution we have 



Pi- 



P 

 instead of the equation 



ition we have 



-Pi _ n/V 2 -b 2 + e\ 



T ~v^bTr ' ' ' A) 



(B; 



Pi— Pi —Vl 



Pi' S' 



which expresses Raoult's law. We see, therefore, that 

 Dr. Tinker's theory, when applied to the case of a dilute 

 solution, gives a law for the lowering of the partial pressure 

 of the solvent quite different from Raoult's law. In his 

 paper, however, Dr. Tinker deduces Raoult's law from his 

 theory. This deduction involves an obvious mathematical 

 error. On pages 433 and 434 he endeavours to prove that 

 for a dilute solution 



7Ti' N 



ir 1 ~ N + n 



Considering the imaginary case of a litre of a decinormal 

 aqueous solution, for which V 2 — b 2 + e = 10(V 1 — bj, Dr. Tinker 

 states : — 



" We have 



1 XT -., - n A V 2 — b 2 + e\ 1 



„=-, N = oo-o, ^1-^-^-] = -^ appro*., 



and N 4- n . 



-jp =lapprox. 



The error in counting — 1 = ^ is thus — . on unity, or 



less than 2 per cent." *> N + ?l 60 



Dr. Tinker here overlooks the fact that deviation from the 

 laws of the ideal dilute solution depends upon the deviation 

 of {tt 1 — 7Ti)I'tti from the value n/N, not on the deviation of 

 TT\\ir\ from unity. In the above imaginary case, we have 



7T 1 ~ 7r/ __ 10n % 



wi 



N 



so that the deviation from Raoult's law, instead of being 

 2 per cent, is 900 per cent. 



