558 COLLECTED STUDIES IN IMMUNITY. 



poison constituents, is out of the question. On the contrary we must 

 assume that the union of these substances with the antitoxin is subse- 

 quently tightened. This tightening is also borne out by other observa- 

 tions, both old and recent. If the toxin-antitoxin reaction were 

 reversible, it should be possible, by removing the supposedly free 

 toxin residue, to constantly change the equilibrium, so that the toxin 

 could all be recovered. Nevertheless, although toxin can be filtered 

 through gelatine and antitoxin cannot, it is impossible either by 

 gelatine filtration (Martin and Cherry) or by gelatine diffusion (van 

 Calcar) to obtain free toxin from neutral toxin-antitoxin mixtures. 1 

 In addition to this one cannot help being surprised that the calcula- 

 tions of Arrhenius and Madsen entirely ignore the cells' toxin-binding 

 receptors which effect the poisoning. In accordance with their 

 views, these receptors should represent an important element in the 

 equilibrium; and yet they appear to have entirely overlooked this 

 fact. 



It would lead us too far to discuss all the arguments against the 

 views of Arrhenius and Madsen. It will suffice to call attention to 

 the serious objections which Nernst has raised regarding the prin- 

 ciples involved, and to Koppe's criticism of their technique in making 

 hsemolytic test-tube experiments. This illustrates the danger of a 

 one-sided mathematical study of biological problems. Even if one 

 succeeds now and then in making the figures of observations and cal- 

 culation tally, it is impossible at the present time for these mathe- 

 matical expressions to explain the facts. To be sure they may be 

 able to represent the resultants of the processes which bring about 

 the phenomena, but in that case the formula is nothing more than 

 an interpolation formula. Corresponding to this, therefore, we see 

 that the formulas of Arrhenius and Madsen vary widely for the same 

 poison, every new lot of poison of the same bacillary origin has a new 

 constant of equilibrium. Hence the formula is applicable only to 

 one particular case, and so, even if it were a correct interpolation 

 formula, progress of biological science would in no way be furthered 

 by it. 



1 It is perfectly evident that toxin can be obtained from fresh toxin-antitoxin 

 mixtures by diffusion through gelatine, and this has recently been demonstrated 

 by Madsen and Walbaum. According to Morgenroth such mixtures require 

 at least twenty-four hours for the union to become complete. Hence the state- 

 ment by Madsen and Walbaum that the mixtures must be fresh in order to 

 demonstrate what they regard as dissociation only confirms our view. 



