RELATIONSHIPS BETWEEN AGGLUTININ, ETC. 



51 



From this equation we observe a third source of error in Eisenberg 

 and Yolk's method of obtaining their "coefficient of absorption." 



After correcting the errors just pointed out, a repetition of the ex- 

 periments performed according to the method of Eisenberg and Volk 

 gives values agreeing entirely with those calculated and this also sub- 

 stantiates the truth of my assumptions and formulae. 



The curves graphically representing the phenomenon of agglutination 

 (see fig. 1) are two straight lines (x — y = 

 B 



and -j x -\- y — C 



0) which interact with 

 each other and fulfill the equation. 



.L. 



Bx z + Axy — AO + ACy — ■ Bxy — Ay" = 



where x is the function of the quantity of 



serum and y that of the degree of agglutination 



(that is, the quantity of agglutinable substance 



AC 

 agglutinated) within the limits of x = -=- and 



r> 



AB 

 y =- — r ^=, i. e., within the limits of the ag- 

 " A + B' ' b 



glutinative power of a serum which contains A 



of agglutinin unit (Ag) and B of agglutinoid 



unit (Ao) in 1 cubic centimeter, C being the 



quantity of bacterial culture in each test tube. 



The serum is also represented by a straight line ao (see fig. 2) 



formula of which is y= —x. 

 A 



the center of coordinates and a having an 

 ordinate =• Ao (agglutinoid unit), while at the 



Oa: = ax — A 



Oy = ex = C 



bx + ex — B 



The equation for the curve 



G P is Ba; 2 + Axy — A.Cx + 



ACj/ — Bxy — Ay- = 



Fig. 1 



the 



The limit of agglutination is a>a, u> being 



point e which has an abscissa 



2 V A + B / 



the 



phenomenon is most complete. The limit of 

 the quantity of agglutinoid which causes the 

 disappearance of agglutination (in the macro- 

 scopical test) is A (X — 1) , where the value of fig. 2. 



X varies according to the kind of bacilli, while the relation between the 

 quantities of agglutinin and agglutinoid required to keep complete agglu- 

 tination with some degree of serum dilution, while both substances are 



A f 



variable, is =5^^ >, where / is the quantity of agglutinated agglutinable 



substance which varies according to the different species of bacilli. 



Serum has a coefficient of viscosity about 300 times greater than that 



