HcEmolytic Activity of Chemical Substances. 



293 



From these are derived the following values for the constants in the 



equations relating «, /3 and 7 to S : — 



a. h. c. m. n. p. 



9 65 20 0-01 16-6 0-04 



The following tables compare calculated and experimental results : — 



8 = 1000. 8 = 2000. 



Texper. Tcalc. Texper. Tcalc. 



10 42 42-3 30 125 127 



30 10-5 10-6 40 47 48 



The general relations between T, t and S, for any of the hfemolytic 

 substances examined, having been dealt with, there remains to be expressed 

 certain relations which exist between the constants of the equations relating 

 «, 13 and 7 to the dilution. These relations hold true for all the substances 

 examined, and probably for most hpemolytic substances. 



It will be seen that the hsemolytic activity of a substance depends 

 principally on the manner in which a and /3 vary with the dilution. The 

 variation of a with the dilution depends chiefly on the value of m, while the 

 variation of /3 with dilution depends chiefly on the value of a. There must, 

 then, be a relation between the value of n and the value of a, for any 

 substance. 



Let ajb — tan ^, 



and 100m = tan w, 



the relations between <^ and w is expressed by a hyperbola, whose equation is 

 0-75a)2 + a)(<^-45)-52 = 0. 



Since 6 is a constant for all htemolytic substances examined (65), from a 

 known value of a the corresponding value of m can be found. 



The relation between « and 3 further depends on the value of the constant 

 n. This constant is related to the value of in. If, as above, 



100 m = tan co, 



the relation between co and 01 is expressed by a rectangular hyperbola, and by 

 the equation, 



71(90-0)) - 750. 



The relation of /3 to the dilution depends to some extent on the value of c ; 

 this constant has a simple relation to the constant p, 



c = 500p. 



The value of c may be readily found for any substance, for which one value 

 of 7 is known. 



z 2 



