S. C. BROOKS 69 



lecular reaction than in the case of a reaction proceeding at a constant 

 rate, and the lengths will be still greater for reactions of higher orders. 

 The relative times, ti and k, required for two reactions with the same 

 initial velocity to reach the same stage, when one is monomolecular 

 and the other has a constant velocity, may be easily derived from the 

 equations of the two time curves. The expression is 



to X a — X 



a 

 where In is the logarithm to the base e (2.3026 logio ■ may advan- 



a — x 



tageously be used in place of In ), and where a is the initial 



amount of the reacting substance, and x the amount transformed at 

 any given stage ; a and x are usually stated in per cent. 



If we compare the rates of hemolysis which would result from the 

 action of two fundamental reactions of different orders, we find that 

 the relative time required to reach a given stage will be the same 

 regardless of the variation curve of the cells affected; if the shape of 

 the variation curve is given by some equation other than y = yo 

 (which gives identical time curves for the fundamental reaction and 

 for the process as a whole), we can still calculate the relative lengths 

 of time required for the process to reach a given stage, according 

 to the order of the fundamental reaction. If the fundamental reac- 

 tion is monomolecular or of a higher order, we must use as abscissae dis- 

 tances which are as much greater than those of the time curve when 

 the fundamental reaction has a constant velocity, as is indicated by 

 calculations like that given above. This is most easily done if it is 

 assumed that the hemolysis and the fundamental reaction reach 

 completion simultaneously, but may still be calculated for a known 

 exdfess or deficiency of the lytic agent. In Fig. 4 are given the courses 

 which would be assumed by a process taking place in a group of cells, 

 the equation of whose variation curve was 



y = yo 



(-s)" 



if the fundamental reaction were {a) proceeding with a constant 

 velocity; (b) proceeding according to the law of monomolecular 



