TOXIN AND ANTITOXIN: METHODS OF THEIR STUDY. 551 



The existence of the toxons which has been deduced mathematic- 

 ally from the biological experiments is, however, no longer based 

 merely on these calculations. At the present time their existence 

 is a proven fact, for quite recently van Calcar succeeded in separately 

 isolating toxin and toxon from the native poison solution by means 

 of a ingenious dialyzing procedure. Owing to its smaller molecular 

 volume, toxin diffuses through a suitable membrane under less ten- 

 sion than toxon. In this way one obtains toxon-free toxin on one 

 side and toxin-free toxon on the other. 



This direct confirmation of the conclusions drawn from the bio- 

 logical analysis of the toxins shows how a mathematical study, pro- 

 vided biological facts are carefully regarded, can get at the nature 

 of the phenomena in question, despite the failure of chemical methods. 

 To be sure the mathematical treatment of biological problems must 

 be undertaken very carefully. The phenomena of animate nature 

 are so manifold, and subject to so much change, that they cannot 

 all be forced into the limits of a formula. It is particularly dangerous 

 to build up formulas and laws on the basis of too simple assumptions. 

 For them one can easily be deceived by the apparent exactness of 

 figures, and arrive at conclusions which do not sufficiently regard the 

 complexity of the actual phenomena. 



Unfortunately these warnings are much needed at the present 

 time, for certain high authorities are striving energetically to explain 

 the most complex phenomena, like those which occur in the union 

 of toxin and antitoxin, as though they were simple and readily cal- 

 culated reactions between simple substances. 



In opposition to the plurality of the poison constituents demon- 

 strated by Ehrlich, Arrhenius and Madsen, as is well known, uphold 

 a Unitarian standpoint. Their deductions are based entirely on 

 the method of partial neutralization introduced into toxin study by 

 Ehrlich and referred to above. Up to this point they differ only in 

 the method of representing their results graphically. For this purpose 

 they use a system of coordinates, laying off the amounts of antitoxin 

 contained in each mixture on the abscissas. But whereas in Ehrlich's 

 scheme the ordinates represent the amounts of toxin which each 

 addition of antitoxin causes to disappear, Arrhenius and Madsen use 

 the ordinates to represent the toxicity which each mixture still retains. 

 In their work these authors observed that now and then in a num- 

 ber of poisons, especially in tetanolysin, the line connecting the points 

 plotted possessed a certain similarity to curves obtained when weak 



