THEORIES OF DYEING 321 



equally in accordance with any theory which involves equilibrium 

 whether chemical or physical. Walker found that the relation 



C < K 



holds for this distribution, but in this particular instance x = 27 

 and K = 35*5 ; that is 



C f 



s yc v 



K = 35*5 ; 



i.e. if the solid solution theory holds, this equation means that 

 the molecule of picric acid in aqueous solution is, on the 

 average, 27 times as great as the molecule of picric acid 

 dissolved in silk. This cannot be so, since a consideration of 

 freezing points and electrical conductivity of aqueous solutions 

 of picric acid shows that the molecule in solution in water is the 

 simplest possible, i.e. it is not only not greater than CoH 2 (N0 2 )3- 

 OH, but is much less than this owing to high electrolytic 

 dissociation. By a simple transformation we get 



Q 



= 35 5 



dC f 1 dC 



logQ = log 35-5 4- — .logC, 



Cf 27 C w 



In this form the equation states that a slight proportionate 

 change in the concentration of picric acid in the water is always 

 accompanied by a corresponding proportionate change in the 

 concentration of the acid in the silk. Thus if the concentration 

 in the water increases by 1 per cent, of its value, no matter what 

 that value is, the concentration in the silk will increase by 



— per cent, of its own value. 



27 l 



Formulae of this kind apply to very many cases of absorp- 

 tion, e.g. Schmidt found a similar one to apply to the 

 absorption of iodine and various acids from solution by 

 animal charcoal, and Kiister for the distribution of iodine 

 between water and starch solution. But it does not, of course, 

 follow from the identity of the formulae valid in these cases 

 that the phenomena themselves are identical in nature. 



Walker and Apbleyard next turned their attention to the 



