52 TOXINES AND ANTITOXINES. 



obtaining a closer insight into the nature of chemical reactions. 

 ARRHENIUS and MADSEN measure the time within which the 

 haemolysis has reached a definite point. 



For this purpose they cause an excess of " toxine " to act for a 

 fixed time upon equal amounts of blood (which are taken as 

 exactly 100). The haemolysis is interrupted by cooling the 

 mixture, which is then separated in a centrifugal machine, and 

 finally the extent of haemolysis is determined. Since the 

 quantity of blood-corpuscles dissolved in the unit of time is the 

 reciprocal of those remaining undissolved (100 - x), the follow- 

 ing equation is obtained : 



(1) J^ = K 

 whence 



It has been shown that K is not a constant, but shows a rapid 

 increase in the course of the experiment. This is due to the fact 

 that the membranes of the blood-corpuscles at first offer resist- 

 ance to the action of the toxine, but that this resistance becomes 

 continually weaker with the destruction of the membrane. 



At first no blood-corpuscles at all are attacked, and it is not 

 until the weakest membranes give way that haemolytic action is 

 apparent. This power of resistance thus leads to the necessity 

 of an "induction period" for haemolysis, the explanation of which 

 is evident in these cases. 



Hence this method did not yield reliable results. Its authors, 

 therefore, tried whether twice the amount of " toxine " in half 

 the time had the same effect as half the amount in twice the 

 time. It was found that, after making the necessary corrections 

 for the alteration in volume, there was this approximate ratio, 

 viz., that the velocity of the reaction was proportional to the concen- 

 tration of the toxine. This held good in the case of ammonia, 

 sodium hydroxide, and tetanolysine. 



The quantity of unaltered blood-corpuscles can be expressed 

 by the following equation (in which a represents the amount of 

 toxine), at all events with low proportions (i.e., where x is 

 small) : 



d x 



after integration 



*/~x = 2 K a t, 



