454 BACTERIOLOGICAL CHEMISTRY 



results, in which all the values except R are known. 

 Similarly the behaviour of the reagents and the com- 

 position of the precipitates in the region of polysaccharide 

 excess can be calculated and the quantitative behaviour 

 of the serum over the whole range can be predicted. 



Kendall has derived the same equation (3) from a 

 consideration of the number of combining groups available 

 for combination and the proportion of them which are 

 actually in combination for varying concentrations of 

 antigen and antibody. 



Heidelberger and Kendall showed that these equations 

 hold not only for the Type III pneumococcus system 

 (which is a hapten-antibody system) but also for R-salt- 

 azo-diphenyl-azo-egg albumin and its antiserum., for 

 crystalline egg albumin and its antiserum and for the 

 Type I pneumococcus polysaccharide system. There was 

 found to be a difference between horse and rabbit pneumo- 

 coccus antisera, possibly due to the difference in molecular 

 weights of the globulins, which are 500,000 for horse 

 globulin and 150,000 for rabbit globulin. For rabbit 

 antiserum to Type III pneumococcus the value of 211 is 

 13-5 and for the horse antiserum 32, giving ratios of 85 

 and 200, respectively, for antibody-protein to poly- 

 saccharide at the equivalence point. Using the above 

 values for the molecular weights of the globulins, the 

 molecular weight of the polysaccharide is thus 1,800 to 

 2,500, corresponding to 5 to 8 aldobionic acid units. 

 In the case of the Type I pneumococcus system the values 

 of 2R are 5-4 and 14-4 for rabbit and horse antisera 

 respectively, giving values for the molecular weight of 

 the Type I polysaccharide of 4,400 to 4,500. It can be 

 calculated from these values that the composition of the 

 precipitate in the equivalence zone of the Type III system 

 with rabbit antisera would be from S3 A 2 to S2A ; at the 



