ANTIGEN -ANTIBODY REACTIONS 



463 



puiiit. This equation covers the range of precipitate 

 given by mixtures with ratios of antibody to antigen 

 from R to 2R,. Similar but more complex equations 

 were deduced for ratios up to 4R. For the region of 

 antigen excess the equation 



(Ki)2A2 



Mg. of S precipitated = 2RiA — . . . (2) 



Total S 



results, where Rj is the ratio of antigen to antibody at 

 the equivalence point. Close agreement between the 

 experimental values and the values calculated from the 

 above equations was found, as the following examples 

 for two antibody preparations show (Table 33) : — 



Table 33 



( After Heidelberger and Kendall) 



K the values for the ratio of nitrogen to polysaccharide 

 in the precipitate at any two points in the region of 

 antibody excess are known (by experiment), then the ratio 

 (R) at the equivalence point can be calculated, since 

 dividing equation (1) by S the equation 



N 



= 2R- 



R2S 



~a" 



(3) 



