120 INFECTION AND RESISTANCE 



NaOH, we would expect a complete neutralization of one by the 

 other, multiple for multiple, and the explanation of Ehrlich based 

 on the assumption of different toxin constituents, of varying affin- 

 ities, and different pharmacological effects, is the only one which will 

 account for the experimental results. Assuming, however, that the 

 reaction is one analogous to that taking place between a weak acid 

 and a weak base such as boric acid and ammonia we have an en- 

 tirely different state of affairs. For here the reaction goes on to a 

 point of equilibrium, and in mixtures containing equivalent amounts 

 of the weak acid and the base there will be present the reaction prod- 

 ucts and also small amounts of unbound free acid and free base. 

 And according to the law of "Mass Action," the quantities of free 

 acid and base present will depend entirely on the masses of the 

 reagents put together. Thus, for each particular mixture of the two, 

 different quantities of the original substances will be found uncom- 

 bined, and, furthermore, the gradual addition of one to the other 

 will not have a neutralizing value in exact proportion to the amount 

 added. Were the toxin-antitoxin reaction analogous to such chemical 

 systems, then we could assume that every mixture of the two sub- 

 stances, whatever the relative amounts, would contain not only the 

 united toxin-antitoxin molecule, but also varying amounts of disso- 

 ciated free toxin and free antitoxin, the quantities of each depending, 

 according to the law of mass action, upon the molecular concentra- 

 tions obtaining in the individual mixture. This, indeed, is the con- 

 ception of toxin-antitoxin union formulated by Arrhenius and Mad- 

 sen. 



Arrhenius and Madsen, 20 21 bearing in mind these conditions,, 

 made comparative studies of the neutralization of tetanolysin by its 

 antilysin on the one hand, and that of ammonia by boric acid on the 

 other. Ammonia, like most bases, is a hemolytic agent, while boric 

 acid, unlike stronger acids, has no hemolyzing properties. For this 

 reason, in mixtures of the two, the toxicity is proportional to the 

 concentration of free ammonia (though, as Arrhenius states, "a cor- 

 rection must be made for the lowering action of the ammonium salt, 

 as indicated by experiments on this action"). Because the reaction 

 between boric acid and ammonia is reversible, that is, the salt formed 

 is dissociated by the hydrolytic effect of the water, there is always 

 present a slight amount of free ammonia even if the largest possible 

 quantities (to saturation) of boric acid are added. (See Arrhenius, 

 "Immunochem.," p. 174.) The curve of toxicity indeed descends 

 as more boric acid is added, but never reaches 0. 



By a modification of the formula expressing the law of Mass 

 Action, Arrhenius and Madsen could calculate the amount of free 



20 Arrhenius and Madsen. Zeitschr. f. physik. Chem., 44, 1903, and 

 Festschrift Kopenhagen Serum Instit., 1902. 



21 Arrhenius. "Immunochemistry," Macmillan, N. Y., 1907. 



