556 COLLECTED STUDIES IN IMMUNITY. 



will then be governed by the law of mass action formulated by 

 Guldberg-Waage, namely, (toxin) .(antitoxin) =k (toxin-antitoxin), in 

 which the brackets denote the concentration, and k the constant of 

 equilibrium to be determined for each poison. 1 All the calculations 

 of Arrhenius and Madsen are based on this formula, and their entire 

 work stands or falls with the applicability of the formula to the sub- 

 ject of toxins. 



The formula, however, is only then applicable if the reaction 

 is really completely reversible, and this is not the case. Thus if mix- 

 tures containing the same amounts of toxin and antitoxin are tested 

 at the end of the reaction, it is easy to convince one's self that the 

 toxicity is dependent not only on the amounts of toxin and anti- 

 toxin, but on the manner of making the mixtures. If to the same 

 amount of antitoxin we add at intervals fractional parts of the toxin, 

 we shall find that the resulting end product is considerably more toxic 

 than if the same amount of toxin is mixed with the antitoxin at once. 

 This holds true even if the toxin is added at the time corresponding 

 to the addition of the last fraction in the former case. Von Dungern 

 was the first to point out the significance of this experiment, in con- 

 nection with an observation made by Danysz, for the question of 

 reversibility. He showed that if this really was a completely reversible 

 reaction between simple substances, as is assumed by Arrhenius and 

 Madsen, we should expect that the same equilibrium should always 

 ensue with the same total amounts of reacting substances, i.e., the 

 toxicity of the end products should always be the same. Any devia- 

 tion from this could occur in the fractioning process only during the 

 course of the reaction ; and then, provided the deviation were a function 

 of the reaction-time, this would be just the reverse of what is actually 

 observed. 2 Hence all those poisons in which this phenomenon of 



1 In their recent publications Arrhenius and Madsen assume that one mole- 

 cule toxin combines with one molecule antitoxin, not to form two molecules 

 of the toxin-antitoxin combination, as the above formula would show, but that 

 two different substances are formed, toxinan and titoxin. To be sure as the 

 equation then reads, (toxin) (antitoxin )= k (toxinan) (titoxin), one objection 

 to the above formula is done away with, but a new hypothesis, lacking all evi- 

 dence whatever, is thus introduced merely for the sake of the formula. 



2 The phenomenon in question therefore shows exactly the reverse of what 

 Arrhenius and Madsen's theory demand. For this reason the limit of error 

 need not be considered, although, owing to the enormous quantitative differences, 

 it would play no role in judging the result. Nor can Arrhenius extricate him- 

 self from the predicament by suggesting that we are dealing with slowly progress- 



