1910.] The Chemical Dynamics of Serum Reactions. 509 
acted upon (in the special case of hemolysis, the number of celis acted upon). 
In equation (1) it was used to denote the ratio «/y (see equation 10). 
Thus Zo) yy (av) 7, (18) 
where E = effect, 
f(x) = a function of the number of cells, or the concentration of stuff 
acted upon, 
ry = internal resistance (e.g., of the cell), 
R = any external resistance, and a function of the temperature. 
Since y/e and «/cz measure the total quantities of amboceptor and 
complement in a serum, the determination of c and z will afford absolute 
values for these two components; 1/c will be the measure of units of 
amboceptor, and 1/cz the measure of units of complement. An increase in z 
will correspond to a decrease or deterioration of complement, and an increase 
in ¢ to a decrease in amboceptor. | 
In immunisation, however, amboceptor is supposed to increase, and 
complement to remain more or less constant. Thus in immunisation there 
would be a decrease in ¢ and a corresponding increase in z. It is on this 
basis that indices of immunity, obtained from experiments in which both 
amboceptor and complement take part, must rest. The present system of 
bacteriolytic and opsonic indices, based on the observation of a single 
dilution of the serum to be investigated, is and must be liable to error. In 
the case of the horse “Rich” the opsonic index for the whole serum had 
fallen, after two years’ treatment with staphylococcus, although I believe 
that the content in amboceptor had actually increased. I would point out 
that an animal such as this one, even although its opsonic (or other 
compound) index had decreased, would be more potent as a source of anti- 
staphylococcic serum than it was when its index was high. Such an animal 
should not be discarded without careful testing. 
This fact is also of extreme importance with regard to treatinent of 
patients by immunising. For instance, the opsonic index obtained by whole 
serum evaluation would fall off in the later stages of a protracted course of 
treatment, even although the serum had gained in amboceptoral content. I 
do not think that this would be a dangerous state of affairs from the patient’s 
point of view, as possibly he may possess resistive power in a potential state, 
but the fact is worthy of note and of research. 
With regard to the value /(m). Throughout this paper, and in my 
experiments, I have taken m to be sufficiently great to absorb all the 
amboceptor used. But other conditions may prevail. For instance, in: 
opsonic experiments there is a limit in the size of the cell, which would 
VOL. LXXXIII.—B. Ze 
