108 THE SIDE CHAIN THEORY 



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 substance 

 6, 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 f , the 100 a's 

 would then unite with the 100 A's, the 20 b's with the 20 B's, and 

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

 fied molecules of b and 18 of c. If, therefore, a second unit of agglu- 

 tinating serum were now added, 20 of the remaining b'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 b and 16 of c, 

 while the 100 ^4'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 ascrib- 

 ing 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 quantities present in the 

 serum do not tally with those in the bacterial emulsion. The Eisen- 

 berg 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 6 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 react- 

 ing substances and the temperature. Chemical equilibrium will 

 result in accordance with the equation 



(Ca) n . (Cb) m =k 



