1910.] The Chemical Dynamics of Serum Reactions. 51 
the lethal dose may be measured in terms of amboceptor. In the fresh state. 
the dose is measured by od, and in the deteriorated by op (fig. 3). 
(c) A third characteristic is in the curious curve which toxicity (as 
ordinate) assumes, as increasing quantities of antitoxin (as abscissa) are 
added. The curve is an / written backwards. At first it is almost flat. 
(ascribed by Ehrlich to prototoxoid), then it descends more sharply, and: 
finally it becomes again flatter. Arrhenius has shown that the flat. finish 
can be explained on the principle of mass action equilibria between toxin 
and antitoxin, but the flat commencement cannot thus be explained. 
Toxicity is inversely proportional to the minimal lethal dose, and is to be 
distinguished from z, which means degree of effect. | 
Minimal lethal dose can be shown in fig. (3) as follows: Let 1 cc. of a 
toxin contain dy+er. We can measure this by or. Thus or=1lec. Now, 
to cause death, ov must be produced to og, the lethal'line, that is to say, the 
minimal lethal dose is og/or c.c., and the toxicity = 1/M.L.D. = or/og. 
Now suppose we have a toxin containing ay+ex in 1 e.c., and that, after 
acting on it with anti-amboceptor, ay is reduced to dy. 
The lethal dose of ayt+ex = 1 cc. (vide fig. 3), 
but the lethal dose of = dy+ex = (oqg/or’) c.c. 
The toxicity is or/og. 
If we assume, as a simple case, that ay is neutralised by a units of 
antitoxin, then the curve of toxicity is flat at first, and becomes more and 
more steep as more antitoxin is added. But if we assume with Arrhenius 
that complete neutralisation never occurs, then this curve is drawn out in its 
final part, and never reaches the abscissa. 
Thus the prototoxoid phenomenon will appear in certain cases, and I 
would add that it is possible that the curve might even commence with 
a rise, v.¢. a toxin might be found which became apparently more toxic: 
on addition of a small quantity of antitoxin. I am not aware that this. 
has been observed. 
These three primary characteristics of toxin and antitoxin have thus been 
shown to be fully described by the equilibrium relation of equation (1) 
taken in conjunction with Arrhenius’s views; the haptophorous group being 
represented by amboceptor, the toxophorous group by complement, and: 
antitoxin by anti-amboceptor. 
Summary. 
1. Amboceptor and complement are opposed in their action on the cell, 
with the proviso that the former acts as a catalyst to the latter. 
2P 2 
