48 OHNO. 



macroscopic method was uniformly employed. Each one of the pro- 

 cedures mentioned above was adopted after critical study and experi- 

 mentation and further studies were made to ascertain the optimum 

 quantity and concentration of salt solution. 



In standardizing the units, a unit of agglutinin (or agglutinoid) was 

 selected as that amount which is contained in a quantity of serum suffi- 

 cient to agglutinate completely 1 milligram of bacterial culture suspended 

 in 0.85 per cent salt solution when the experiment is conducted for 

 twenty-four hours at 37° C. Complete agglutination was defined as 

 that reaction which results in sedimentation of all particles with clearing 

 of the fluid. For the purposes of experiment it is assumed that one 

 unit of agglutinin will always combine with a certain fixed amount of 

 agglutinable substance. Having established a definite and exact tech- 

 nique by these studies and having critically reviewed similar studies 

 of Joos, Eisenberg and Folk and others, experiments follow which are 

 used in the elaboration of formulas representing the values of agglutinin 

 A and agglutinoid B in 1 cubic centimeter of agglutinating serum. 

 The formulae established are as follows: 



A 



CM (G 



— m) 



M- 

 Cm(M- 



■m 

 -G) 





M — 

 1 G — 

 X~M — 



m 

 m 

 ■m 



In these equations : 

 A = the number of agglutinin units (Ag) contained in 1 cubic centimeter of 



serum tested. 

 B = the number of agglutinoid units (Ao) contained in 1 cubic centimeter of 



serum. 

 C = the weight in milligrams of the agglutinable substance contained in each 



tube, namely the weight contained in 0.5 milligram of bacteria. 



-p = the highest serum dilution in which complete agglutination occurs. 



— == the serum dilution iust too low to cause a visible agglutination but still 

 m 



causing invisible agglutination. 

 =f= = the serum dilution just too high to cause visible agglutination but still 



causing invisible agglutination. 



C 11 



=p = the quantity of substance agglutinated at a seruni dilution of — or =rr. 



The correctness of the above equations was established by proving 

 through them the following propositions : 



1. The value of X must always be the same with the same bacterial culture, 

 notwithstanding all modifications which mav occur in the serum. 



