CHEMICAL NATURE OF ANTIGEN-ANTIBODY INTERACTION 115 



in their antibody forming power; we may assume that the number of 

 agglutinable molecules in a unit of bacterial emulsion is different from 

 that of the various agglutinins in a unit of the corresponding serum. 



Supposing, now, that in the former there were present 100 mole- 

 cules of the agglutinable substance a, 50 of the agglutinable sub- 

 stance b, and 20 of c, while in the antiserum there were present for 

 each unit 100 molecules of agglutinin A, 20 of B, and 2 of C, the 

 100 o's would then unite with the 100 A's, 20 6's with the 20 B's, 

 and the 2 c's with the 2 C"s. There would then be remaining 30 

 unsatisfied molecules of b and 18 of c. If, therefore, a second unit 

 of agglutinating serum were now added, 20 of the remaining 6's 

 would take up the 20 newly added B's and 2 of the remaining 18 

 c's the 2 new portions of C. There would now remain 10 molecules 

 of 6 and 16 of c, while the 100 A's from the second agglutinating 

 unit would be left over. This would represent exactly what we see 

 in the table above, viz., that even though agglutinins in excess be 

 present the bacterial emulsion can still take up more agglutinin if 

 more is added. 



The reason* for this apparent paradox is now, of course, self- 

 evident, and lies in the fact that we have been mentally in the habit 

 of ascribing the agglutinating properties of a given serum to a single 

 substance; whereas there is good evidence to show that this is not 

 necessarily the case, that on the contrary the agglutinating effect 

 may be due to a number of so-called partial agglutinins, to which 

 a similar number of agglutinogens correspond, and that the quan- 

 tities present in the serum do not tally with those in the bacterial 

 emulsion. The Eisenberg phenomenon is thus merely the expression 

 of the coexistence in the mixture of free antigen on the one hand 

 and free antibody on the other, the antigen being in excess merely 

 because not enough antibody has been added. 



Such a coexistence may, however, also be explained in still other 

 ways, showing that there is really nothing unusual in the phenomenon. 

 According to the Guldberg-Waage law of mass action, the quantity 

 of two chemically reacting substances a and b and their product c 

 which may be found at any one time in coexistence depends upon 

 a certain constant k, which varies only with the nature of the reacting 

 substances and the temperature. Chemical equilibrium will result 

 in accordance with the equation 



(Co)" . (Cfr) , 

 (Cc) 



