Hcemolytic Activity of Chemical Substances, 289 



the relation between T and t is expressed by a hyperbola, of which one 

 asymptote is the straight line T = 0. The relation is therefore described by 

 the equation 



r = I [/3-T] + ^. 



where a, /3, and 7 are constants which depend on tlie quantity of haemolytic 

 substance whose action the hyperbola describes. 



In order to find by experiment, within the limits of experimental error, 

 the values of «, /?, and 7 for a given quantity of heemolytic substance, the 

 following procedure is used : — • 



(1) Find by experiment the time taken by this quantity of haemolytic 

 substance to produce hfemolysis of 1 c.c. of standard blood suspension, when 

 To = any value near 0. Gall this time To. 



(2) In a similar manner find Ti, when ti = any value near 10. 



(3) Similarly find T2, when to = any value between 30 and 45. 



(4) Treat that part of the hyperbola which describes the relation between 

 T and r, when t is any value from to 10, as a straight line, which will pass 

 through the points To and Ti : determine the intercepts made by this line on 

 the axes of T and t respectively. The intercept on the T axis will equal /3 ; 

 that on the r axis will equal «. 



(5) Filling in the values of a and /3, obtained as above (4), and the values 

 of T2 and T2 obtained experimentally in (3), in the equation 



find the value of 7 for the hyperbola describing the relation between T and r, 

 for the particular quantity of haemolytic substance under investigation. 



The equation expressing the relation between T and t for any given 

 quantity of haemolytic substance may thus be found from three experiments. 

 The values of «, /3 and 7 obtained should be checked by comparing experi- 

 mental and calculated values of T, when r = 20, t = 30, t = 40, and t = 50. 

 If « and l3 are accurately determined, an excellent correspondence between 

 calculated and experimental results will be obtained. 



In investigating the haemolytic action of a substance, the equations for 

 hyperbolas representing the relation between T and t, in the case of each of 

 several dilutions of the substance, are obtained. A series of values of a, yS, 

 and 7 are thus found, corresponding to various dilutions : these constants 

 may then be expressed as functions of the dilution. 



