■290 Mr. E. Ponder. A Method for Investigating the 



General Uquations relating «, ^, and j to the Dilution. 



In the cases of all the hasmolytic substances examined, these constants are 

 related to the dilution in a similar way : — 



(1) The constant a is a linear function of the dilution. If 8 be the 

 number of cubic centimetres which contains 1 grm. of the haemolytic agent, 

 in the dilution investigated, then the relation between a and S is expressed 

 by an equation of the form 



« = + n, 



where m and n are constant for the particular hseraolytic substance. 



(2) The constant /3 is related to S by a curve. If on the curve points, pi, 

 _P2, Ps, etc., corresponding to values, Si, 82, S3, etc.) be joined to the origin 

 ^ = 0, S = 0, a series of angles 61, 62, 03, etc., will be formed between the 

 joining lines and the abscissa. These angles, expressed in degrees, are 

 related to Bi, B2, S3, etc., by a hyperbola : the relation being expressed by the 

 equation 



0-01S = |[5-^]+^, 



since the hyperbola has one asymptote, the straight line ^ = 0. The relation 

 between /3 and 8 is therefore expressed by the equations 



0-OlS = «-^ + |, (i) 

 a 



0-01 S = /Stan ^, (ii) 



where a, b and c are constant for the particular haemolytic substance. 



(3) The relation between 7 and S is expressed by an equation of the form 



7 = pS, 



where ^ is a constant for the particular hsemolytic substance. Since «, /S, 

 and 7 are related to the dilution in these ways, by a knowledge of the 

 equations given above, and of the values of a, b, c, m, n, and p, for a 

 haemolytic substance, it is possible to calculate the time taken by any 

 dilution of that substance to produce complete haemolysis of 1 c.c. of 

 standard blood suspension, at any given temperature, or to make other 

 calculations involving these variables. 



In order to illustrate these general relations, the results obtained from an 

 examination of the haemolytic action of three substances will be given in 

 detail. The substances selected — saponin, sodium taurocholate, and lactic 

 acid — are chosen because they are examples of a highly haemolytic agent, a 

 moderately hsemolytic agent, and a feebly haemolytic agent respectively : — 



