The main interest of the present investigation lies in the application of well known methods of biological assay to quantitative studies of complement fixation.

A linear relationship was established between the logarithm of the amount of serum and the number of C′H50 fixed by a constant, optimal amount of cardiolipin antigen. Based upon this linearity, the dose-response curves for 11 different sera were compared. Regression lines with a common slope were calculated for 8 of these sera. As tested by the analysis of variance, these lines agreed with the experimental data within the limits of chance variation. The regression lines for 2 other sera, although exhibiting a different slope, could also be considered as parallel.

The potencies of 7 sera and their respective standard errors were calculated in relation to one serum, taken as a reference standard.

It is pertinent to mention that the only previous statistical treatment of complement fixation data known to us is that of Thompson (10), based on results furnished by the method of Wadsworth, Maltaner and Maltaner. From theoretical considerations, Thompson showed the possibility of establishing valid estimates of potency from dose-response curves under conditions other than those of straight lines intersecting at 0 dose, or parallel straight lines. The experimental data which conform to Thompson's model were obtained, however, by a method entirely different from the one adopted in this investigation.

Further work is required to establish the validity of the present method for the comparison of potencies of syphilitic sera, as well as for its application to other immune systems.

1

A preliminary presentation of this paper was given at the Sixth International Congress for Microbiology, Rome, Sept. 6–12, 1953.

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