TOXIN AND ANTITOXIN: METHODS OF THEIR STUDY. 555 



a procedure, in order to possess any justification whatever, would 

 have to be based on an enormous experience. But even aside from 

 this it is amazing to see how a lot of experimental protocols, going 

 back to 1897, are unhesitatingly used for their calculations. The old 

 determinations of the lethal dose, in which death produced acutely 

 in 3 to 4 days was the criterion, are very difficult to make use of 

 owing to the individual variations in the animals. Certainly it re- 

 quires some experience to know which animals should be discarded 

 because of over- or undersusceptibility. But how much more com- 

 plex the conditions really are is at once apparent if one attempts to 

 determine ^ or ^ of a lethal dose from the clinical course of the disease. 

 Hence it is not surprising to find that the lethal doses calculated 

 by Arrhenius and Madsen represent the averages of figures which 

 often differ from each other by many times. The tedious work 

 which these authors have undertaken may perhaps satisfy a mathe- 

 matician , to the biologist, however, it can only represent useless 

 and dangerous playing with figures. It signifies nothing, therefore, 

 if the figures recently obtained by this method by Arrhenius and 

 Madsen with three poisons fail to show any prototoxoid zone. 1 For 

 the same reason, also, we cannot regard certain other figures, which 

 differ markedly in observation and calculation , as arguments against 

 their views. 



However, we need neither confirmation nor controversion of 

 their theory. For it has been found that the assumptions on which 

 this theory is based have no existence whatever. We have already 

 alluded to the fact that van Calcar has recently demonstrated the 

 existence of toxons. But it has also been shown by another method 

 that diphtheria poison, as well as most other toxins, must contain 

 various constituents capable of binding the antitoxin. This method 

 had its inception in the following considerations. 



Arrhenius and Madsen, as already stated, regard the union of toxin 

 and antitoxin as a reversible reaction between two simple [einheitlich] 

 substances. According to this view, therefore, the reaction is incom- 

 plete, i.e., the two substances reacting (toxin and antitoxin) are 

 never completely used up, a certain portion of both toxin and anti- 

 toxin always remaining free beside the neutral toxin-antitoxin combi- 

 nation. The equilibrium which exists between the three components 



1 We should not neglect to mention that the existence of the prototoxoid 

 zone and its development from the hemitoxin phase has also been demonstrated 

 in diphtheria poison by so excellent a worker as Theobald Smith. 



