I go MANUAL OF BACTERIOLOGY. 



the bluer the color. Let A represent, then, a certain amount of antitoxin; 

 let A be capable of combining i, z, 3, 4, 5, different amounts of toxin; call 

 these amounts of toxin T,, T^, T^, T,, T^; and assume that a combination in 

 which all the ^'s are combined with T's in the proportion of ATi, is neutral, 

 that it has no poisonous properties; that a combination represented by AT^ 

 also has no toxic properties, but that A T-^ would begin to show toxic properties, 

 and that ATt is distinctly toxic, and that AT^ is very toxic. Starting with 

 toxin, then, if just enough antitoxin is added to neutralize its poisonous proper- 

 ties, AT I is first formed, which is not toxic; now add more toxin, and none of 

 this remains free, but, on the contrary, AT^ is formed, which is not toxic; on 

 adding stiU more, when ATi °^ ^^5 's reached the mixture is fatal for guinea- 

 pigs. The paralysis which EhrHch attributes to toxon would be represented, 

 say, by ATy In between the combinations represented by ATi to AT^ are 

 all imaginable combinations, a sliding scale of no definite units. 



In other words, while Ehrlich holds that toxin and antitoxin unite in one 

 definite proportion, Bordet holds that they may unite in any proportions, like 

 two different colors of paint mixed together producing any intermediate color 

 with more or less tint of one or other of the two original colors. 



The evidence adduced by Bordet for this conception is very abundant and 

 fully repays study. 



Still another theory offered to explain the peculiar behavior of the antitoxin- 

 toxin mixture is advanced by Arrhenius and Madsen, also supported by 

 experimental evidence. They also deny the existence of toxon, and look upon 

 a mixture of antitoxin and toxin as analogous to an amphoteric mixture of a 

 dilute acid and alkali, or of an acid and alcohol. In such combinations there 

 are compounds formed of the two substances, but some of each of the two con- 

 stituents remains free. An ester is not only a compound formed by an acid 

 and an alcohol, but it has free alcohol and free acid. Moreover, the ester is 

 constantly changing, some of the alcohol and some of the acid separating and 

 new ester constantly forming again. . When first mixed, more ester is formed, 

 and less alcohol and acid are liberated, till a point of dynamic equiUbrium is 

 reached, when just as much ester is formed as there are alcohol and acid hber- 

 ated. Just so in adding toxin to antitoxin: at first more of the two combine 

 than is set free, but after a time a condition of dynamic equilibrium is estab- 

 lished, and any additional toxin remains free. 



Briefly stated, these are the three theories which are now advanced by com- 

 petent authorities, and, if these outlines are kept clearly in mind, it will not be 

 difficult to understand the subject as presented in the many medical journals 

 and the many monographs which have appeared on the subject.* 



* A summary will be found in a monograph by Michaelis. Die Bindungs- 

 gesetze von Toxin und Antito.xin. BerUn. 1905. Also a special article en- 

 titled, Immunity. Journal of the American Medical Association. Nos. 4 et 

 seq. 1905. 



