RELATIONSHIPS BETWEEN AGGLUTININ, ETC. 49 



2. The value of A and of B must be constant or nearly so, even if we vary the 

 value of C within limits which do not cause X to change. 3 



3. The quantity of bacterial culture uniting with agglutinin at any particular 

 degree of reaction can be established and remains about the same, when we use 

 the same bacterial suspension, notwithstanding all modifications which may occur 

 in the serum. 



4. Having determined the quantities of bacterial culture uniting with agglu- 

 tinin in the different grades of reaction, the value of "m" can be calculated from 



the known amount of agglutinated substance concerned in the antephase of j% 

 dilution of the serum. 4 



5. In the same way the value of M can be calculated from the known value of 



agglutinated substance concerned in the postphase at _ dilution of the serum. 



6. The value of G can be calculated from the known value of agglutinated 



substance at ± dilution in the antephase of _ . 

 D M 



The failure of other investigators in their attempts to find the law 

 governing the agglutination phenomena and to express it in a mathe- 

 matical equation, proceeds in part either from their selection of stand- 

 ards of measurement which are not sufficiently accurate, or from their 

 adoption of unsuitable units, or, as in the cases of Bisenberg and Volk 

 and Craw and Joos, from their allowing too short a time for complete 

 agglutination to occur. The preliminary steps which led to my dis- 

 covering the formula for agglutination were, first, my assumption that 

 agglutinin, agglutinoid and agglutinable substance always unite according 

 to a fixed ratio; second my adoption of suitable units; third, my adop- 

 tion of a scale expressing the degrees of agglutination with a fair degree 

 of accuracy; fourth, my assumption that agglutinoid is present to some 

 extent in every agglutinating serum; and fifth, my assumption that 

 every reaction of agglutination is accompanied by a certain amount of 

 invisible agglutination. 



As the result of their studies, Eisenberg and Volk insist that the 

 combining ratio of agglutinin and agglutinable substance varies accord- 

 ing to the quantities employed and they express this fact by means of 

 their "coefficient of absorption." My investigations lead to the conclu- 

 sion that these experimenters have three constant errors in their exper- 

 iments, first, their neglect of agglutinoid; second, their failure to take 

 into account the degeneration of agglutinin, produced by the temperature 

 during the agglutination test; and third, their failure to appreciate the 

 difference between the quantity of united (fixed) agglutinin and that 

 of agglutinated agglutinin. 



3 If the value of C is too high or too low, the density of the bacterial emulsion 

 in the test tube is so much changed that it is not possible to determine exactly 



Q 



the point represented by ^ . 



4 — = the degree of dilution of the agglutinating serum in any one given test tube. 



66027 4 



