8 4 



ARRHENIUS' AND MADSEN's VIEWS 



The heavy line represents the curve of neutralization on 

 Ehrlich's principles, and apparently shows the presence of a 

 large number of varieties of toxin with different combining 

 capacities. When, however, the neutralization was carried out by 

 the addition of very small quantities of the antitoxin at a time, 

 the curve became a hyperbola of the character seen in the dia- 

 gram. Further, having found the value of k by determining by 

 experiment the amount of toxin left free after the addition of 

 a certain amount of antitoxin to a certain amount of the toxic 

 solution in two different instances, and hence, by use of the 

 formula : 



Free toxin free antitoxin _ (toxin x antitoxin) 

 vol. vol. vol. 



the amount of free toxin after any addition of antitoxin could be 

 calculated theoretically. It could then be determined by experi- 

 ment, and the results compared. In one case given by Arrhenius 

 and Madsen this was done, with the following result : 



The correspondence is certainly very close. 



The case of diphtheria toxin was next investigated, and in the 

 figure which follows the " stair-step " curve, showing Ehrlich's 

 conception of its constitution, shows the presence of proto-, deutro-, 

 and trito-toxins, and of toxon. The curved line is that calcu- 

 lated after the constant of dissociation had been determined by 

 experiment. 



