116 THE SIDE-CHAIN THEORY 



in which a and b represent the reacting substances, c their product, 

 C, the concentration, and n, m, and o the respective number of 

 molecules. If we conceive that only one molecule of the reacting 

 substance enters into play the equation may be simplified so as to 

 read 



Ca . Cb 



Cc 



= k 



As k is constant it will be seen that by increasing the concentra- 

 tion of either a or 6 the concentration of the product also must be 

 increased. If, now, we conceive k to be infinitesimally small or even 

 equal to zero, then the concentration of either a or b or of both must 

 be zero, since c itself cannot be zero. In this case we would come to 

 an end reaction where both a and b would be completely used up 

 and only the product remain. If, on the other hand, k is infinitely 

 large, then the concentration of c must be correspondingly small, and 

 if k = oo then c must equal 0, which means that no union whatever 

 occurs between a and 6. Between these two extremes, viz., k = 

 and k = GO , an infinite number of variations is, of course, possible, 

 and it is thus readily conceivable that k in the case of the agglu- 

 tinin-agglutinable substance reaction may be of such a value that 

 a partial reaction only is possible between the two. This, of course, 

 is what we see in the Eisenberg phenomenon, and accepting this 

 explanation we would have additional proof that the reaction between 

 antigen and antibody is actually of a chemical character. 



Still another explanation is possible on the basis of the so-called 

 law of distribution. This is based upon the following considerations: 

 If a given substance a is soluble in two solvents A and B, and if the 

 substance in question is brought together with A and B simulta- 

 neously, a certain amount will be dissolved in A and a certain amount 

 in B. The ratio between the two amounts is a constant which varies 

 only with the nature of the substance in question and the tempera- 

 ture, but which is uninfluenced by the initial concentration. From 

 a study of the figures given by Eisenberg (see above), Arrhenius 

 concluded that the peculiar relationship between the amount of agglu- 

 tinin present in the free state and that taken up by the bacteria 

 could be readily accounted for on the basis of the law of distribution, 

 and he developed for this particular case the equation 



(Quantity of bound agglutinin) 3 _ 

 (Quantity of free^iufinin)' ~ k ^constant) 



