540 OSTERHOUT— DYNAMICAL THEORY OF ANTAGONISM. 



the value of K^. We may assume that the amount of this substance 

 increases as CaCL increases and that its maximum effect on K^ is 

 produced in 95.24 NaCl + 4.76 CaCU, after which a further increase 

 of this substance produces less and less effect on Kn. Or we may 

 assume that the decrease of K^ is directly proportional to the 

 amount of this substance but that the maximum amount of this sub- 

 stance is produced in 95.24 NaCl -|- 4.76 CaCL, while in other mix- 

 tures it is produced in lesser amounts. Let us consider more fully 

 the latter alternative. 



The simplest assumption which we can make is that both NaCl 

 and CaClo combine with some substance. X, in the protoplasm so as 

 to form a compound. If we suppose that this compound^'' is 

 Na2o-X'CaCl2o formed by the reversible reaction 



2oNaCl + X + CaCL ^ Na^oAXaCU, 



we can calculate the amount of Naoo^CaCloo which will be formed 

 in each mixture of NaCl -f- CaCL. 



The molecular concentration of X can hardly be more than a 

 small fraction of that of NaCl and CaCU. Hence as NaCl and 

 CaCL are present in great excess they may be regarded as constant 

 in concentration and we need only consider the changes in X and 

 Na^oXCaCLo. 



We may calculate the amounts of Na^o^CaCLo formed at equi- 

 librium in any mixture by means of the formula 



ConCNa,oXCaCl»» 



A = 



(ConcNaci)^°(Conccaci2)(Concx) ' 



in which i^ is a constant and the molecular concentrations of 

 Na2o-^CaCl22, NaCl, CaCL, and X are denoted by the abbreviation 

 Cone. We find that the amount of NajoACaCLo begins with o in 

 pure NaCl, increases with the increase of CaCL until it reaches a 

 maximum at NaCl 95.24 -J- CaCL 4.76 and then decreases (as CaCL 

 continues to increase) until it falls to o in pure CaCL. As this is 

 exactly what K2 does, we might assume that Na2oXCaCL2 acts 

 as a negative catalyzer, causing a decrease in Ko which is directly 

 proportional to the amount of Naoo-X^CaCLo. 



10 Such compounds are frequently formed between salts and proteins 

 as well as with many other amphoteric electrolytes. 



