112 THE SIDE-CHAIN THEORY 



of the bacillus; as experience, moreover, has shown that different 

 antigens, even though closely related, may differ very considerably 

 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 aerglutinin A, 20 of B, and 2 of C, the 

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

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

 unsatisfied molecules of 6 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 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 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 quantities 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 



