38 LECTURES ON IMMUNITY 



ular reaction. If now the initial concentration of the 

 second group of reacting molecules is termed B, we get 



which, if B is very large compared with x and with A, gives 

 the same solution as the differential equation for the mono- 

 molecular reaction, K^ KB. 



In many cases, for instance in the inversion of cane 

 sugar, the one reacting molecule (the hydrogen ion) is 

 reformed by a secondary process so rapidly that its con- 

 centration may be regarded as independent of the progress 

 of the reaction. In this case, belonging to the so-called 

 catalytic processes, we may also apply the formula for 

 the monomolecular reaction, putting K proportional to the 

 concentration of the unchanged molecules (here the 

 //"-ions). 



If A = B, the differential equation of the bimolecular 

 reaction gives the solution : 



i i 



As a special case may be regarded that in which two mole- 

 cules of the same kind react with each other. 



If n molecules all at the same concentration react with 

 each other (the so-called ;/-molecular reaction), we find 



which gives the solution : 



n-l \n-l 



